Question

`solve the following logarithmic equation: log _(12) (x-3) - log_(12) (x+7)=log_(12)3`

Answer 1

`\bf log_(12)(x-3)-log_(12)(x+7)=log_(12)(3)\\\\ -----------------------------\\\\ log_{{ a}}\left( (x)/(y)\right)\implies log_{{ a}}(x)-log_{{ a}}(y)\qquad thus\\\\ -----------------------------\\\\ log_(12)\left( \cfrac{x-3}{x+7} \right)=log_(12)(3)\impliedby \begin{array}{llll} \textit{removing the log from}\\ \textit{both sides} \end{array} \\\\\\ \cfrac{x-3}{x+7}=3\implies x-3=3x+21\implies -24=2x\implies -12=x`