To solve the equation 0.125 * 8^(2x-5) = (√2/4)^-4, we need to simplify both sides of the equation first.
0.125 8^(2x-5) = 1/8 8^(2x-5) = 8^(-3) * 8^(2x-5) = 8^(2x-8)
(√2/4)^-4 = (2^(1/2)/4)^-4 = 2^(-2/4 * 4) = 2^-1 = 1/2
Now our equation becomes:
8^(2x-8) = 1/2
Taking the base 2 logarithm of both sides:
log2(8^(2x-8)) = log2(1/2)(2x-8) log2(8) = log2 (1/2)(2x-8) 3 = -16x - 24 = -16x = 23x = 23/6
Therefore, the solution to the equation is x = 23/6.
To solve the equation 0.125 * 8^(2x-5) = (√2/4)^-4, we need to simplify both sides of the equation first.
0.125 8^(2x-5) = 1/8 8^(2x-5) = 8^(-3) * 8^(2x-5) = 8^(2x-8)
(√2/4)^-4 = (2^(1/2)/4)^-4 = 2^(-2/4 * 4) = 2^-1 = 1/2
Now our equation becomes:
8^(2x-8) = 1/2
Taking the base 2 logarithm of both sides:
log2(8^(2x-8)) = log2(1/2)
(2x-8) log2(8) = log2 (1/2)
(2x-8) 3 = -1
6x - 24 = -1
6x = 23
x = 23/6
Therefore, the solution to the equation is x = 23/6.