How do I find the exact solution to this equation?

Question

Hi! Can you help show me how to solve this?

log5(x-2) = -1

Answer 1

This problem uses a basic property of logs, namely 10^{log x} = x

So we have 10^{log (5x-2)} = 10^-1 = .1 so

5 ( x - 2 ) = .1 and x - 2 = .02

So x = 2.02 Check

5 ( x-2 ) = 5 (.02 ) = .1 and log (.1) = -1

Answer 2

log means 10 to what power. So 10 to what power=5?

On the calculator hit 5 log; you'll get .6987. To check hit 10^.

So .6987(x-2)=-1.

-1/.6987=-1.43068

x=1.43068