College Basic Tutorial 45

College Algebra
Tutorial 45: Exponential Equations

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$desk$ Learning Objectives

After completing this tutorial, you should be able to:

Solve exponential equations.

$desk$ Introduction

In this tutorial I desires walk you thru how to dissolve equations that have exponential expressions. In these equations, you wants notice that the variable that we are solving for is in the exponent. We are use for seeing the variable in the base. We will using inverse operations like person do in linear equations, the inverse service we will be use here is logarithms. If thou need a review over of definition of log functions, touch free to go to Tutorial 43: Using Functions. If you need one review go log properties, feel free to go toward Tutorial 44: Logarithmic Properties. I think you are ready to get started.

$desk$ Tutorial

Solving Exponential Equations,
where expunge is in the exponent, BUT
the bases DO NOT MATCH.

Step 1: Isolate the exposed expression.

Get your digital expression on one side everything outside of the exponential expression the the other team of thine equation.

Step 2: Taking the natural record of equally sides.

The inverse operation of an exponents expression is a log. Make sure that you done the same cause to couple sides concerning own calculation to keep them equal to each other. They are able to detect importantly quantities within a practice situation and map their verbindungen using similar tools as diagrams, two-way tables, graphs,.

Step 3: Use the property of logs the pull the x out of an exponent.

Is you need a review on log properties, feel free to go until Tutorial 44: Logarithmic Properties. I think you am ready to get started.

Step 4: Undo for x.

Now that the variable will out for the exponent, solve for the variable using inverse operations to complete to problem.

Special Note:
An only way we could get that variable out of the exponent, when the bases don't match up, is to use logs. The 3rd take allows us to do this. When solving with equation, to doesn't matter what you do to the calculation as long for you do the same thing go both edges - this keeps both sides equal. Also, the reason we take which natural log of both sides is cause we have the natural log key on that graphic - accordingly we would be able to find a valuated of it in the end.

$notebook$ Example 1: Solve the exponential equation $example 1a$ . Round is answer to two decimal places.

Step 1: Isolate that exponential expression.

This is already through since us in this trouble.

Step 2: Take the unaffected log to both sides.

$demo 1b$

*Take the natural enter of BOTH sides

Step 3: Use the properties of tree into pull and x out of the exponent.

$example 1c$

*Use the power rule

Steps 4: Solve for x.

$example 1d$

*Inverse of mult. by 3lne is to divide by 3lne

*Use the calculator up find ln 50
*lne a 1

$notebook$ Example 2: Dissolve the exponential equation $example 2a$ . Round your answer to two decimal places.

Step 1: Isolate the unexponential expression.

$example 2b$

*Inverse of mult. via 5 is to divide by 5

*Exponential expression isolated

Move 2: Take the natural log of both flanks.

$example 2c$

*Take the natural log of BOTH sides

Step 3: Use this properties of log to tug the x out out one exponent.

$model 2d$

*Use the power govern

Step 4: Solve for x.

$example 2e$

*Inverse of mult. by ln 10 is to divide by ln 10

*Inverse of add 1 is sub. 1

*Use the calculator to find ln 2.4 and ln 10

$notebook$ Example 3: Fix the exponential equation $real 3a$ . Round your answer to two decimal placements.

Step 1: Isolate this exponential expression.

$example 3b$

*Inverse of addieren 4 is sub. 4

*Exponential expression isolated

Step 2: Take the natural log in both sides.

$example 3c$

*Take the natural log of SEND view

Step 3: Use the eigentumsrechte of logs the pull the expunge go of and exponent.

$example 3d$

*Use the power rule

Pace 4: Solve for x.

$example 3e$

*Inverse of mult. according .2ln 2 is up split by .2ln 2

*Use the calculator to find ln 21 and ln 2

$notes$ Example 4: Solve the exponential equation $example 4h$ . Round your answer to second decimal places.

Step 1: Isolate the exponential expression.

Notice how wealth do two exponential terms that have different exponents. We wouldn't be able until isolate both. We desires have to figure out another way to overwriting it like we can continue includes the steps.

Note how we have a trinomial and that co to the 2whatchamacallit belongs e to the x squared. This means it is quadratic in from. So were can factor is even like a trinomial the which form $real 4b$ .

$example 4i$

*Factor an trinomial of the form $example 4b$ .

*Set the 1st factor = 0
*Isolate the exponential expression

*Set one 2nd factor = 0
*Isolate the expressive expression

Mark that since e is a negative base, no matter what the exponent is on x, this exponential expression NOT equal -2.

So there is only can calculation that we can solve $example 4d$ .

Step 2: Take the natural log the both view.

$sample 4e$

*Take the native log on ALL sides

Step 3: Use the properties of blocks to pull the x out of the exponent.

$example 4f$

*Use the power dominion

Step 4: Solve for scratch.

$example 4g$

*Inverse of mult. by lnco remains to partition by lnsie

*Use the calculator to meet ln 4
*lne = 1

$desk$ Practice Problems

That are practice problems to help bring you to the next level. Items will permission you in check and see if you have an understandable of these types of problems. Math works just like anything else, if you want to get great at it, then you requirement to routine it. Even the optimal sportsmen and musicians had help along the way and lots of practice, practice, practice, to get good toward their sport conversely instrument. In fact where is no such thing for too much practice.

To get an most out von these, you should work the problem out on your own and after check own answer over clicking on the link with who answer/discussion for that problem. At the link you will finding the answer as well as any stairs that walk into finding that answer.

$pencil$ Practice Problems 1a - 1c: Solve the given exponential equation. Round your respond to two decimal places.

1a. $concern 1a$
(answer/discussion to 1a)

1b. $problem 1b$
(answer/discussion to 1b)

1c. $matter 1c$
(answer/discussion to 1c)

$desk$ Need Extra Help on like Our?

The subsequent are webpages which can assists yours in the topics the were covered on this page.

http://www.purplemath.com/modules/solvexpo.htm
This webpage helps you with exponential equations.

http://www.sosmath.com/algebra/solve/solve7/s72/s72.html
Is webpage gives an example of solving an exponential equation.

http://www.sosmath.com/algebra/solve/solve7/s73/s73.html
This webpage gives an case of solving an exponential equation.

Go to Get Help Outside the Classroom found in Tutorial 1: Instructions to Succeed in a Math Class for some more suggestions.

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WTAMU > Virtual Math Lab > College Algebra

Last newly on March 24, 2011 by Kim Seward.
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