algebra

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

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  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!

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