Question

$2\times {81}^x=3\times {36}^x,$ then $x=\frac{1}{m},m=$

Answer 1

$2\times {81}^x=3\times {36}^x$ then $x=\frac{1}{m},m=$

$\frac{2}{3}={\left(\frac{36}{81}\right)}^x$

$\frac{2}{3}={\left(\frac{6^2}{9^2}\right)}^x$

$\frac{2}{3}={\left(\frac{6}{9}\right)}^{2x}$

$\therefore {\left(\frac{2}{3}\right)}^1={\left(\frac{2}{3}\right)}^{2x}$

$1=2x$

$\therefore x=\frac{1}{2}=\frac{1}{m}$

$\therefore m=2$