Respuesta :
bearing in mind that for the "change of base" rule, it doesn't matter what base one uses, so long is the same atop and below.
[tex]\bf \textit{Logarithm Change of Base Rule} \\\\ log_a b\implies \cfrac{log_c b}{log_c a} \\\\\\ \textit{Logarithm Cancellation Rules} \\\\ \boxed{log_a a^x = x}\qquad \qquad a^{log_a x=x}\\\\ -------------------------------\\\\ log_{25}(125)\implies \cfrac{log_5(125)}{log_5(25)}\qquad \begin{cases} 125=5^3\\ 25=5^2 \end{cases}\implies \cfrac{log_5(5^3)}{log_5(5^2)} \implies \cfrac{3}{2}[/tex]
[tex]\bf \textit{Logarithm Change of Base Rule} \\\\ log_a b\implies \cfrac{log_c b}{log_c a} \\\\\\ \textit{Logarithm Cancellation Rules} \\\\ \boxed{log_a a^x = x}\qquad \qquad a^{log_a x=x}\\\\ -------------------------------\\\\ log_{25}(125)\implies \cfrac{log_5(125)}{log_5(25)}\qquad \begin{cases} 125=5^3\\ 25=5^2 \end{cases}\implies \cfrac{log_5(5^3)}{log_5(5^2)} \implies \cfrac{3}{2}[/tex]
