# Real world logarithm problems worksheet

You're describing numbers in terms of their powers of 10, a logarithm. And an interest rate is the logarithm of the growth in an investment. Surprised that logarithms are so common?

Me too. Also, can you imagine a world without zinc? Math expresses concepts with notation like "ln" or "log". Finding "math in the real world" means encountering ideas in life and seeing how they could be written with notation. Don't look for the literal symbols! When was the last time you wrote a division sign?

When was the last time you chopped up some food? How did this happen? It might not be the actual cause did all the growth happen in the final year? We can think of numbers as outputs is " outputs" and inputs "How many times does 10 need to grow to make those outputs?

Large numbers break our brains. Millions and trillions are "really big" even though a million seconds is 12 days and a trillion seconds is 30, years.

It's the difference between an American vacation year and the entirety of human civilization. The trick to overcoming "huge number blindness" is to write numbers in terms of "inputs" i. This smaller scale 0 to is much easier to grasp:. A 0 to 80 scale took us from a single item to the number of things in the universe. Not too shabby. Logarithms describe changes in terms of multiplication: in the examples above, each step is 10x bigger.

With dilation and translation calculator natural log, each step is "e" 2. When dealing with a series of multiplications, logarithms help "count" them, just like addition counts for us when effects are added.

We're describing numbers in terms of their digits, i. Adding a digit means "multiplying by 10", i. Logarithms count the number of multiplications added onso starting with 1 a single digit we add 5 more digits 10 5 andget a 6-figure result. Talking about "6" instead of "One hundred thousand" is the essence of logarithms.

It gives a rough sense of scale without jumping into details. Bonus question: How would you describe ,? Saying "6 figure" is misleading because 6-figures often implies something closer toWould "6.

Not really. In our heads, 6. With logarithms a ". Taking logwe get 5. Try it out here:. We geeks love this phrase.Username: Password: Register in one easy step! Reset your password if you forgot it. Algebra: Logarithm Section. Solvers Solvers. Lessons Lessons. Answers archive Answers. In t years an investment will grow to the amount expressed by the functionwhere t is time in years. See the plot in Figure 1.

Figure 1. Divide both side of this equation by the initial amount of You get an equation. Take logarithm base 10 from both sides. Apply the Power Rule to the logarithm. Therefore, approximately 12 years. Note that this result is in agreement with the plot in Figure 1. Population Growth An initial number of bacteria presented in a culture is This number doubles every 30 minutes. Figure 2. Graph of the function Solution 1 The function expressing the bacteria growth iswhere is an initial number of bacteria in the culture, t is time in minutes.

The plot for the ratio is shown in Figure 2. Divide both sides by N 0the initial number of bacteria. Therefore, approximately minutes.

Note that this result is in agreement with the plot in Figure 2. Radioactive decay Polonium Po has a half-life of days. Figure 3. Graph of the function Solution 1 The decay function for Polonium P iswhere is an initial amount of Polonium P in the sample, t is time in days. The plot for the ratio percentage is shown in Figure 3. Therefore, approximately The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year.

This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories. For our opening exercise I will have my students participate in an activity where they are given several commands.

Each command will limit them in some way shape or form. They will have to carry out each command while taking into consideration that limitation. The commands will be presented on a card of some sort. Because my classroom is set up in tables, I will give each student at each table a different card. No student at the same table should have the same card.

The cards will have the following scenarios written on them:. Every student will be given a whiteboard paddle to write their answers on. When I read their scenario, they will come to the front of the classroom with their paddles and present their answers. It is my hope that I will get several different answers for most of these scenarios so that we can discuss why each scenario has more than one possible solution.

After these students have presented their answers and we have had the discussion as to why there is more than one solution to the scenario being presented at that time, I will then ask all students what are some other possible solutions. This activity is designed to help students to prepare for today's lesson by helping them to see how inequalities can be used in context.

Today, I will show my students real-world scenarios that involve inequalities. During instruction, I will ensure that my students understand that the solution will provide a range of answers. Students should be able to locate key words and phrases and understand what those key words and phrases direct them to do.

To do this, I will present my students with two problems that I will work out step by step. One problem is a word problem that involves inequalities. The other problem is one that will require me to work backwards to create an inequality word problem. The modeling of these two problems will later serve as a reference to the successful completion of the independent practice. For this reason, all students should be taking notes during this time.

Using these problems, I will allow student to ask questions and address any misconceptions that they may have at this time. Students will be given 5 minutes to complete 2 inequality word problems that mirror the problems that I modeled for them during the instructional piece of this lesson.

During this time, I will be traveling the room answering any questions that the students may have, ensuring that they have a good grasp of the concept and are ready to move on. After the allotted time has elapsed, I will ask my students to provide the solution to the first problem.

Then, I will ask three students to provide me with solutions to the second problem. The students that I choose for the second problem will be selected using a purposeful method, in that, they will be chosen to showcase the many different ways that the students could have solved this particular problem. During the first task, I will give my students 4 mathematical scenarios involving inequalities to solve. These mathematical scenarios will be presented to my students on a worksheet and requires my students to write a one-step inequality when given a mathematical scenario and then solve that one-step inequality.

This task is great for a quick assessment as to my students' ability to break down and solve inequality word problems. For the second task, my students will be required to write a mathematical scenario involving inequalities in the same manner as what was presented during the instructional portion of this lesson.There are two main 'shapes' that a logarithmic graph takes.

Can you figure out why? Below you can see the graphs of 3 different logarithms. As you can tell, logarithmic graphs all have a similar shape. Has an asymptote that is a vertical line :.

Grow very slowly for large X explore with this applet. Based on the table of values belowexponential and logarithmic equations are:.

## Inequalities in the Real-World

Remember: Inverse functions have 'swapped' x,y pairs. There are many real world examples of logarithmic relationships. Logarithms graphs are well suited. Logarithm Worksheets. Logarithm Graph Applet Explore graph, graph of inverse and its properties. Property 1 All logarithmic graphs pass through the point.

Property 2 The domain is: All positive real numbers not zero. Property 3 The range is: all real numbers.

### Logarithm Examples and Practice Problems

Property 4 It is a one-to-one function. All real numbers. Property 5 Has an asymptote that is a vertical line :. Property 6 Grow very slowly for large X explore with this applet. Property 7 Does not have horizontal asymptotes.

### Free Math Printable Worksheets with Answer Keys and Activities

Inverse functions! Can you identify which equation below represents a logarithmic equation? Show Answer. Logarithmic graphs. When you are interested in quantifying relative change instead of absolute difference.

Consider for instance the graph below. When you want to compress large scale data. Consider for instance that the scale of the graph below ranges from 1, toon the y-axis and 1 to on the x-axis--such large scales which can be typical in scientific data are often more easily represented logarithmically. Read more at wikipedia about this. Popular pages mathwarehouse. Surface area of a Cylinder. Unit Circle Game. Pascal's Triangle demonstration. Create, save share charts. Interactive simulation the most controversial math riddle ever!Logarithm worksheets in this page cover the skills based on converting between logarithmic form and exponential form, evaluating logarithmic expressions, finding the value of the variable to make the equation correct, solving logarithmic equations, single logarithm, expanding logarithm using power rule, product rule and quotient rule, expressing the log value in algebraic expression, logarithms using calculator and more.

There are two sections in each worksheet. The first section is about converting logarithmic form to exponential form. Second section is vice versa.

Solving Logarithmic Equations - Example 1

Sheet 1 Sheet 2 Sheet 3 Grab 'em All. Solve the problems involving more logarithmic expressions. Take enough practice with level 1 and come back here. Solve the logarithmic equations and find the value of the unknown variables. On easy and moderate levels, you will end up with linear equations after canceling out the logarithms. Difficult level contains quadratic equations. Applying the logarithm rules, such as product rule, quotient rule and power rule, rewrite each expression in single logarithm or expanded form. Sheet 1 Sheet 2 Sheet 3. Each variable is assigned with a logarithm.

Translate each logarithmic expression into algebraic expression. Use calculator to find the value of each logarithm.

## Lesson Using logarithms to solve real world problems

Round the answer to two decimal places. Mixed type contains a both common and natural logarithm. Rewrite each logarithm by applying the change of base rule; find the value using the calculator. Members have exclusive facilities to download an individual worksheet, or an entire level. Login Become a Member.

Logarithmic and Exponential Form There are two sections in each worksheet. Single Logarithm and Expansion Applying the logarithm rules, such as product rule, quotient rule and power rule, rewrite each expression in single logarithm or expanded form.

Sheet 1 Sheet 2 Sheet 3 Download All Solving Equations using Calculator Using either antilogarithm method or exponential form method, solve each logarithmic equation. What's New?

Follow us. Not a Member?Downloading Link is given at Last. Real life scenario of logarithms is one of the most crucial concepts in our life. As we know, in our maths book of 9thth class, there is a chapter named LOGARITHM is a very interesting chapter and its questions are some types that are required techniques to solve. To know about the real-life scenario of logarithms we start as an earthquake intensity measurement.

For this, first we let to know some knowledge related to the earthquake measurement instrument known as Seismograph. In the earthquake, a Seismic wave produces which travels through the Earth layer.

The seismic wave gives out an energy that causes the earth to shake and also gives out low frequency acoustic energy. Read More : Maths Short Tricks Now, these seismic waves is recorded by the seismograph instrument and its output is the seismographs graph.

This occurs directly beneath the epicenter, at a distance known as the focal depth. The amplitude of the seismic waves decreases with distance. This is commonly known as the Richter scale. T he magnitude of an earthquake is calculated by comparing the maximum amplitude of the signal with this reference event at a specific distance.

The Richter scale is a base logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude. The magnitude of the standard earthquake is. Read: Why Log is not defined for the negative base. For example: if we note the magnitude of the earthquake on the Richter scale as 2, then the other next magnitude on the scale is explained in the following table. Now according to the Richter scale magnitude of the earthquake, there is a lot of bad effect on our environments which may be a danger to the real world.

Its details are given below in the table. Richter Magnitude Description Earthquake Effects This is one of the real-life scenario of logarithms, which must be known. To know this concept in detail, click here. Now, according to physics rule, the sound intensity is measured in terms of loudness which is measured in terms of a logarithm. Thus the sound intensity is defined as the. In this definition, dB is the decibels.

It is one-tenth of bel B and I and I 0 are the sound intensity. Hence, we can different values. To solve these types of problems, we need to use the logarithms. The solving method of these problems will be learning in another maths blogs post. The URL of the post will be mentioned below in the future. Practice: Logarithm Questions Set 1. You must be logged in to post a comment. Monday, April 13, Real Life Scenario of Trigonometry. Related Articles. Leave a Reply Cancel reply You must be logged in to post a comment.Downloading Link is given at Last.

Real life scenario of logarithms is one of the most crucial concepts in our life. As we know, in our maths book of 9thth class, there is a chapter named LOGARITHM is a very interesting chapter and its questions are some types that are required techniques to solve. To know about the real-life scenario of logarithms we start as an earthquake intensity measurement. For this, first we let to know some knowledge related to the earthquake measurement instrument known as Seismograph.

In the earthquake, a Seismic wave produces which travels through the Earth layer. The seismic wave gives out an energy that causes the earth to shake and also gives out low frequency acoustic energy.

Read More : Maths Short Tricks Now, these seismic waves is recorded by the seismograph instrument and its output is the seismographs graph.

This occurs directly beneath the epicenter, at a distance known as the focal depth. The amplitude of the seismic waves decreases with distance. This is commonly known as the Richter scale. T he magnitude of an earthquake is calculated by comparing the maximum amplitude of the signal with this reference event at a specific distance.

The Richter scale is a base logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude. The magnitude of the standard earthquake is. Read: Why Log is not defined for the negative base. For example: if we note the magnitude of the earthquake on the Richter scale as 2, then the other next magnitude on the scale is explained in the following table. Now according to the Richter scale magnitude of the earthquake, there is a lot of bad effect on our environments which may be a danger to the real world.

Its details are given below in the table. Richter Magnitude Description Earthquake Effects This is one of the real-life scenario of logarithms, which must be known.

To know this concept in detail, click here. Now, according to physics rule, the sound intensity is measured in terms of loudness which is measured in terms of a logarithm.

Thus the sound intensity is defined as the. In this definition, dB is the decibels. It is one-tenth of bel B and I and I 0 are the sound intensity. Hence, we can different values. To solve these types of problems, we need to use the logarithms. The solving method of these problems will be learning in another maths blogs post. The URL of the post will be mentioned below in the future. Practice: Logarithm Questions Set 1. You must be logged in to post a comment. Thursday, April 9, Real Life Scenario of Trigonometry.