Question

(1/5)^(x-2)=125

Answer 1

If you think about it, 1/5 is really 5^-1, which is read "five raised to the negative one."

125 becomes 5^3.

We needed to have the SAME BASE of 5 on BOTH sides of the exponential equation.

We now have this:

5^-1(x - 2) = 5^3

NEXT:

Remove the parentheses from the left side by applying the distributive rule on the exponent.

-1(x - 2) = -x + 2.

We now have this:

5^(-x + 2) = 5^3

Here comes the easy part--->bring down the exponents and solve for x.

-x + 2 = 3

-x = 3 - 2

-x = 1

x = 1/-1

x = -1

How do we know that x = -1?

Let's plug -1 for x in the ORIGINAL question given and simplify.

If we get the same answer of 125 on BOTH sides, then we will know
that x = -1.

Ready?

You were given this:

1/5^(x - 2) = 125

Let x = -1.

1/5(-1 - 2) = 125

1/5^(-3) = 125

1 divided by 1/5^3 = 125

1 divided by 1/125 = 125

125/1 = 125

125 = 125

It checks!!!

Final answer:

x = -1

Done!