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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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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 = 282 = 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.