3^x + 5^x = 12

I have taken logs on both sides, used the power rule to get

xln3 + x ln5 = ln12

factored out x on the LHS to give x(ln3 + ln5) = ln12

combined logs

x(ln15) = ln12

divided through by ln15

x = (ln12)/(ln15)

The answer I get doesnt match what I want. Where have I gone wrong please?