Question

Log d
√xy8
9
Z


Need help figuring this one out

Answer 1

`\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 rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\[-0.35em] ~\dotfill`

`\log_(d)\left( \cfrac{√(x)y^8}{z^9} \right)\implies \log_(d)\left( \cfrac{x^{(1)/(2)}y^8}{z^9} \right)\implies \log_(d)(x^{(1)/(2)}y^8)-\log_(d)(z^9) \\\\\\ ( ~~ \log_(d)(x^{(1)/(2)})~~ + ~~ \log_(d)(y^8) ~~ )-\log_(d)(z^9)\implies \cfrac{1}{2}\log_(d)(x)+8\log_(d)(y)-9\log_(d)(z)`