Math- Algebra II

SOLVE..
Please show the steps so I'll understand it
8^x-2=(1/16)

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  1. 8^(x-2) = (1/16)
    first, we can observe that both 8 and 16 are powers of 2, thus we express 8 and 1/16 as 2 raised to some power:
    8 = 2*2*2 = 2^3
    1/16 = 1/(2*2*2*2) = 1/(2^4)
    recall that when a certain number raised to an exponent is on the denominator, and we want it to be on the numerator, we make the exponent have the opposite sign, for example:
    1/(3^2) = 3^(-2)
    2/(5^3) = 2*5^(-3)
    5/(2^(-2)) = 5*2^2
    thus we can rewrite 1/(2^4) as
    1/(2^4) = 2^(-4)
    rewriting the equation:
    8^(x-2) = (1/16)
    2^[3(x-2)] = 2^(-4)
    since they now have the same base (which is 2), we can equate their exponent:
    3(x-2) = -4
    3x - 6 = -4
    3x = 2
    x = 2/3

    hope this helps~ :

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