How do I solve for x in 2(27)^x = 9^(x-1)? Thank you!
2(3^3)^x = (3^2)^(x-1)
2(3^(3x) ) = 3^(2x-2)
log both sides
log[2(3^(3x) ] = log 3^(2x-2)
log 2 + (3x)log 3 = (2x-2)log 3
log2 + (3x)log3 = 2x log3 - 2log3
3xlog3 - 2xlog3 = -log(3^2) - log2
xlog3 = -(log9+log2)
x = -log18/log3 = appr -2.6309