Solving an exponential equation Alright, here's the equation:
$$‎1.08^x = 1.10^{x-1}$$
I know I need to use logarithms, but I can't figure how to do it.
Thanks in advance!

Don't get hung up on the fact that the bases don't match. The so-called power rule (or exponent rule) for logarithms works for any base.
$$
\begin{align*}
1.08^x &= 1.10^{x-1}\\
\ln\left(1.08^x\right) &= \ln\left(1.10^{x-1}\right)\\
x\ln(1.08) &= (x-1)\ln(1.10)\\
x\ln(1.08) &= x\ln(1.10) - \ln(1.10)\\
x\ln(1.08) - x\ln(1.10) &= - \ln(1.10)\\
x(\ln(1.08) - \ln(1.10)) &= - \ln(1.10)\\
x &= \frac{-\ln(1.10)}{\ln(1.08) - \ln(1.10)}
\end{align*}
$$
