Question

Write the expression as a single logarithm PLEASE

(log3-log4)-log2

Answer 1

`\bf \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{(3)/(4)}{~~2~~} \right) \\\\\\ \log\left( \cfrac{(3)/(4)}{~~(2)/(1)~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)`