I fear that this equation cannot be solved symbolically.

That would be correct, if the original equation had been .I have taken logs on both sides, used the power rule to get

xln3 + x ln5 = ln12

That's correct, provided, as I wrote above, the original equation really was .factored out x on the LHS to give x(ln3 + ln5) = ln12

combined logs

x(ln15) = ln12

divided through by ln15

x = (ln12)/(ln15)

Either you have gone wrong in the very first step when you assumed that , or you have gone wrong in believing that the solution that you have found is not correct (or, rather, that it is "not what you want").The answer I get doesnt match what I want. Where have I gone wrong please?