Question 1033654

your equation is 3^(2x) = 2^(x-1)
take the log of both sides of the equation to get:
log(3^(2x)) = log(2^(x-1))
since log(a^b) = b*log(a), your expression becomes:
2x * log(3) = (x-1) * log(2)
simplify to get 2x * log(3) = x * log(2) - log(2)
subtract x * log(2) from both sides of the equation to get:
2x * log(3) - x * log(2) = - log(2)
factor out the x on the left side of the equation to get:
x * (2 * log(3) - log(2)) = - log(2)
divide both sides of this equation by (2 * log(3) - log(2)) to get:
x = - log(2) / (2 * log(3) - log(2))
simplify to get:
x = - .4608454206
that should be your answer.
replace x with that in the original equation of 3^(2x) = 2^(x-1)
you will get .3632801844 = .3632801844
that confirms the solution is correct.