**Equations Involving Logarithms and Exponentials**

**Sol A**
.

**Sol B** Dividing by 5 gives , and then taking natural logarithms
of both sides gives
or . Therefore
, so
.

**Sol C** Factoring
gives
, so either
or . If , then . Since for all values of
, has no solution; so is the only solution.

**Sol D**
. (Notice that this answer checks in the original equation.)

**Sol E**
or . Since does not satisfy the
original equation, is the only answer.

**Sol 1**
or .
Since does not check in the original equation, is the only answer.

**Sol 2**
or , so or .

**Sol 3**
or . Since
does not check in the original equation, is the only answer.

**Sol 4** Factoring
gives
, so either
or . Taking natural logarithms gives or .

**Sol 5**
.

**Sol 6**
or . Since
does not check in the original equation, is the only answer.

**Sol 7** Dividing both sides of
by 3 gives
, and then taking natural logarithms of both sides gives
. Then
, so
and therefore
.

Thus , which we can also write as .

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