Question

Logarithms 8^(x-9) = 19^(3x+2)

Answer 1

$\bf 8^{x-9}=19^{3x+2}\implies log(8^{x-9})=log(19^{3x+2}) \\\\\\ (x-9)log(8)=(3x+2)log(19)\impliedby distributing \\\\\\ xlog(8)-9log(8)=3xlog(19)+2log(19) \\\\\\ xlog(8)-3xlog(19)=9log(8)+2log(19)\impliedby \textit{common factor} \\\\\\ x[log(8)-3log(19)]=9log(8)+2log(19) \\\\\\ x=\cfrac{9log(8)+2log(19)}{log(8)-3log(19)}$