Question

I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.

Ex: 12^3 = (x^4)*(y^3)*(z^6)
Can anyone explain how to make that a logarithmic equation?

Answer 1

`\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill`

`12^3~~ = ~~x^4 y^3 z^6\implies \log_(12)(x^4 y^3 z^6)=3 \\\\\\ \log_(12)(x^4)~~ + ~~\log_(12)(y^3)~~ + ~~\log_(12)(z^6)~~ = ~~3 \\\\\\ 4\log_(12)(x)~~ + ~~3\log_(12)(y)~~ + ~~6\log_(12)(z)~~ = ~~3`