# Logarithmic and Exponential Equations

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## Solving Logarithmic Equations

To solve logarithmic equations we take advantage of the properties of logarithmic functions and the fact that

We also use the additional fact that if then M = N for M, a, N positive numbers and

## Example

Solve:

Now we just need to make sure our answers make sense. When x = -7, we have which cannot occur since the domain of the logarithm function is

## Solving Exponential Equations

In a similar fashion to solving logarithmic equations, we can solve exponential equations by using their properties and the fact that if

Example:

Solve:

We start by dividing both sides by 8 to get . Taking the log base 3 of both sides we find that . Finally by our properties of logarithms .

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