Question

If f(x)=log10x, what is the approximate value of y in the equation 10^y=5?

Answer 1

$\bf log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -----------------------------\\\\ 10^y=5\implies log(10^y)=log(5)\implies ylog(10)=log(5)\\\\\\ y=\cfrac{log(5)}{log(10)}\\\\ -----------------------------\\\\ \textit{Logarithm Change of Base Rule}\\\\ log_{{ a}}{{ b}}\implies \cfrac{log_{{ c}}{{ b}}}{log_{{ c}}{{ a}}}\\\\ -----------------------------\\\\ y=\cfrac{log(5)}{log(10)}\iff y = log_{10}(5)\iff y=log(5)$