A^B=C^D

A^B=C^D

Find D

$\begin{array}{|rcll|} \hline C^D &=& A^B \quad &| \quad \ln() \text{ both sides }\\ \ln(C^D) &=& \ln(A^B) \quad &| \quad \ln(a^b) = b\cdot \ln(a) \\ D\cdot \ln(C) &=& B\cdot ln(A) \quad &| \quad :\ln(C) \\ \mathbf{D} & \mathbf{=} & \mathbf{B\cdot \frac{ln(A)}{ln(C)}} \\ \hline \end{array}$

ln(a*b)/ln(c)