Question

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

Answer 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~ :