The equations in Solving Simple Log Equations Algebraically involved simple logarithmic expressions. You were able to convert the logarithmic form into exponential form and then solve the equation. Not all log equations will be that simple. Here are the two types of equations we will practice solving in this section:

1. Logs on both sides of the equation.

   log₄ (2x − 3) = log₄ x + log₄ (x − 2)

2. Multiple logs on only one side of the equation.

   log₃ (9x) − log₃ (x − 8) = 4

These should look more complicated than the log equations we solved before, and it will take a few more steps to solve them algebraically.

Example 1

Solve the equation log₄ (2x − 3) = log₄ x + log₄ (x − 2).

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Check Your Answer

x = 3

Watch the video below for a solution to this equation:

Example 2

Solve the equation log₃ (9x) − log₃ (x − 8) = 4.

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Check Answer Here

x = 9

Watch the video below for a solution for this equation.

Now that you've seen the two examples with more complicated log equations, try solving these problems on your own. You should use scratch paper and your calculator. Click to reveal the solutions.

(1)    log2 (x − 3) + log2 (x + 2) = log2 (4x)	(2)    log (2x − 5) − log (10 − x) = 1
Interactive popup. Assistance may be required. Check Your Answer	Interactive popup. Assistance may be required. Check Your Answer