Question

How do you solve `5^ { m - 1} - 5= 27`?

Answer 1

`m = log(5^2(1+3^3/5))/log(5)`

Explanation:

`5(5^(m-2)-1)=3^3`

`5^(m-2)-1=3^3/5`

`5^(m-2)=1+3^3/5`

`5^m=5^2(1+3^3/5)`

`m log(5)=log(5^2(1+3^3/5))`

`m = log(5^2(1+3^3/5))/log(5)`