Verified answer

log5(4x-7) = log5 (x-2) + 1

log_5 (4x -7) - log_5 (x -2) = 1

log_5 * [ (4x-7) / (x - 2) ] = 1

(4x - 7) / (x -2) = 5

4x - 7 = 5(x -2)

4x - 7 = 5x - 10

4x - 5x = -10 + 7

-x = -3

x = 3

I assume 5 is the base,

log5 (4x-7)/(x-2)=log5 5

4x-7=5x-10

3=x

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Double Check:

log5 5=log5 1 +1

1=1

God bless you.

raise everything to a base 5

4x-7 = 5^ [log_5(x-2) + 1]

the logs will cancel out and you can solve using algebra

4x+7 = (x-2)5

4x + 7 = 5x - 10

x = 17