`log_8(5-12x)=log_8(6x-1)` Solve the equation. Check for extraneous solutions.

We are asked to solve

`log_8(5-12x)=log_8(6x-1)`

Exponentiating both sides with base 8 we get:

5-12x=6x-1
18x=6

x=1/3.

This is in the domain of both expressions of the equality (the domain for the left hand side is x<5/12 and the domain of the right side is x>1/6).

Checking the answer we get `0=log_8(5-4)=log_8(2-1)=0`

The answer is x=1/3.

The graph:

Comments

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