Question

How do you solve `5^x = 25^(x-1)`?

Answer 1

First thing we should know is;
`25^b=(5^2)^b=5^(2b)` This is a basic rule to be memorised.
So our question is;
`5^x=25^(x-1)`
We can write it as ;
`5^x=(5^2)^(x-1) => 5^x= 5^(2*(x-1)) => 5^x=5^(2x-2)` Since bases (5 values) are same. We can write;
`x=2x-2 => ul (x=2)`