Question

Evaluate the logarithm. Log_6 1/36

Answer 1

`\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\\\ \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -------------------------------\\\\ log_6\left( (1)/(36) \right)\implies log_6\left( (1)/(6^2) \right)\implies log_6\left( 6^(-2) \right)\implies -2\cdot log_6(6) \\\\\\ -2\cdot 1\implies -2`