Question

B12%7D%20%28x%2B7%29%3Dlog_%7B12%7D3" id="TexFormula1" title="solve the following logarithmic equation:
log _{12} (x-3) - log_{12} (x+7)=log_{12}3" alt="solve the following logarithmic equation:
log _{12} (x-3) - log_{12} (x+7)=log_{12}3" align="absmiddle" class="latex-formula">

Answer 1

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