Question

Ln a+3 + ln a-3 = ln 16

Answer 1

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\\\\ and\qquad \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -----------------------------\\\\ ln(a+3)+ln(a-3)=ln(16)\implies ln[(a+3)(a-3)]=ln(16) \\\\\\ ln[a^2-3^2]=ln(16)\impliedby \textit{removing ln() from both sides} \\\\\\ a^2-9=16\implies a^2=16+9\implies a^2=25 \\\\\\ a=\pm\sqrt{25}\implies a=\pm 5$