solve for x 8=6^x using logs

I suppose you mean x to the 8th power Take the 1/8 root of both sides. I will assume base 10, but the choice of a base won't affect the answer.

x^8 = 6^x
x = [6^(1/8)]^x = (1.25103)^x
log x = x log 1.25103 = 0.09727 x
This is still a transcendental equation. I had to solve it by iteration, and got x = 1.354