Question

Simplify 6log6 15

A. 4.701849846e+11
B. 90
C. 15
D. 6

Answer 1

`\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] ~\dotfill`

`6\log_6(15)\implies \log_6(15^6)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_(10)(15^6)}{\log_(10)(6)}}\qquad \approx \qquad 9.068\qquad \approx\qquad 9`