Question

Rewrite the following using one or more properties of logarithms and evaluate.

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ log\left( \cfrac{1}{10^{-3}} \right)+log(10^4)\implies log(10^3)+log(10^4)\implies log(10^3\cdot 10^4) \\\\\\ log(10^{3+4})\implies log(10^7)\implies log_{10}(10^7)\implies 7$