Question

Rewrite and simplify ln(4500) in terms of ln5 and ln6

Answer 1

$\bf \textit{logarithm of factors}\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\\\\\ \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -------------------------------\\\\ 4500\implies 6\cdot 6\cdot 5\cdot 5\cdot 5\implies 6^2\cdot 5^3 \\\\\\ ln(4500)\implies ln(6^2\cdot 5^3)\implies ln(6^2)+ln(5^3)\implies 2ln(6)+3ln(5)$