Question

log x 8 = 0.5

Answer 1

One approach is to express 0.5 as a power of 8 and 3 as a power of 27.

0.5 = 2^-1
2 = 8^(1/3)
So 0.5 = [8^(1/3)]^(-1) = 8^(-1/3)
Thus log_8[8^(-1/3)] = -1/3.

Do the other one the same way, since 3 = 27^(1/3).

Another approach is to use the log conversion formula, which you might or might not have seen.

log_8(0.5) = log_2(0.5)/log_2(8) = (-1)/3

In general, log_a(x) = log_b(x)/log_b(a) for any a and b.