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Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
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Properties of Exponents
Solving Equations with Log Terms on Each Side
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Estimating Products and Quotients of Mixed Numbers
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Multiplication Property of Radicals
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Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
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Solving a System of Three Linear Equations by Elimination
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Introduction to Fractions
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Adding and Subtracting Rational Expressions with Different Denominators
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Finding The Greatest Common Factor
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Solving Equations Containing Rational Expressions
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Solving Equations with One Log Term

We can solve many equations that contain a logarithm by converting from logarithmic form to exponential form.

To change forms we will use the following fact: logbx = L is equivalent to bL = x

For example, log232 = 5 is equivalent to 25 = 32.

 

Example 1

Solve: log 8 x = 2

Solution

Rewrite in exponential form.

Simplify.

log 8 x = 2

82 = x

64 = x

So, log 8 64 = 2. This checks because 82 = 64.

Note:

Notice that the equation logbx = L is NOT solved for x.

To solve for x, we rewrite it as bL = x.

Here is another way to check our solution of log8x = 2.

log8 x = 2

Is log8 64 = 2 ?

Is log8 82 = 2 ? (Recall logbbn = n.)

Is 2 = 2 ? Yes

 

Example 2

Solve: ln x = 3.5. Round your answer to two decimal places.

Solution

Write ln x as loge x.

Rewrite in exponential form.

Simplify using a calculator.

 ln x =

loge x =

e3.5 =

 x

3.5

3.5

x

33.12

So, ln 33.12 ≈ 3.5.

To check the solution, compute ln 33.12 on a calculator. The display should read 3.50013733, which is approximately 3.5.

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