**Equations Involving Logarithms and Exponentials**

Recall that if , then

.

(Notice that is undefined if .)

We will denote natural logarithms (logarithms with base ) by .

Furthermore, .

**Ex 1** Solve the equation
.

**Sol**
or . Since does not
check in the original equation, is the only solution.

**Ex 2** Solve the equation
, and write your answer using
natural logarithms.

**Sol** Dividing by 6 gives , and then taking natural logarithms
of both sides gives
or
. Then
, so
and therefore
. Since , we can also write the
answer as
.

**Pr A** Solve the equation
.

**Pr B** Solve the equation , writing your answer using
natural logarithms.

**Pr C** Find all solutions of
.

**Pr D** Solve the equation
.

**Pr E** Find all solutions of
.

**Pr 1** Solve the equation
.

**Pr 2** Solve the equation
.

**Pr 3** Solve the equation
.

**Pr 4** Solve the equation
.

**Pr 5** Solve the equation
.

**Pr 6** Solve the equation
.

**Pr 7** Solve the equation
, and write your answer
using natural logarithms.

Go to Solutions.

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