### Concept (1)

Sometimes we are given exponential equations with different bases on the terms. In order to solve these equations we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in **exponential equations with different bases** by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.

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Sample Problems
(8)

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###### Problem 1

Solving an exponential equation with negative exponents by taking the common log of both sides.

###### Problem 2

Solving an exponential equation by taking the natural log of both sides.

###### Problem 3

Solving an exponential equation by taking the common log of both sides.

Solve:

7^{x + 1} = 9^{x − 4}

###### Problem 4

Solving an exponential equation by taking the common log of both sides and then factoring to obtain an answer.

###### Problem 5

Different methods of solving exponential equations with different bases

###### Problem 6

How to solve exponential equations with different bases that can not be rewritten as the same base.

###### Problem 7

How to solve for x in an exponent by two methods

###### Problem 8

How to solve logarithmic equations with two different bases and x in two separate exponents.