Question

Write the expressions without using log. Can someone please help with this?

Answer 1

$\bf \textit{logarithm of factors}\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\\\\\ \textit{Logarithm of rationals}\\\\ log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y) \\\\\\ \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -------------------------------$

$\bf log(m^3n)\implies log(m^3)+log(n)\implies 3log(m)+log(n) \\\\\\ \boxed{3k+v} \\\\\\ log\left(\cfrac{m}{n^3} \right)\implies log(m)-log(n^3)\implies log(m)-3log(n) \\\\\\ \boxed{k-3v}$