Question

Find all the solutions for x: log3 4 -log3 x=2

Answer 1

`\bf \textit{Logarithm of rationals}\\\\ log_{{ a}}\left( (x)/(y)\right)\implies log_{{ a}}(x)-log_{{ a}}(y) \\\\\\ \textit{Logarithm Cancellation Rules}\\\\ log_{{ a}}{{ a}}^x\implies x\qquad \qquad {{ a}}^{log_{{ a}}x}=x\\\\ -------------------------------\\\\`


`\bf log_3(4)-log_3(x)=2\implies log_3\left( (4)/(x) \right)=2\impliedby \begin{array}{llll} now\ we\\ exponentialize\\ both\ sides \end{array} \\\\\\ 3^{log_3\left( (4)/(x) \right)}=3^2\implies \cfrac{4}{x}=3^2\implies \cfrac{4}{9}=x`