Calculate: 6^{x-13}=7^x

Expression: ${6}^{x-13}={7}^{x}$

Take the logarithm of both sides of the equation

$x-13=\log_{ 6 }({ 7 })x$

Move the constant to the right-hand side and change its sign

$x=\log_{ 6 }({ 7 })x+13$

Move the expression to the left-hand side and change its sign

$x-\log_{ 6 }({ 7 })x=13$

Factor out $x$ from the expression

$\left( 1-\log_{ 6 }({ 7 }) \right)x=13$

Divide both sides of the equation by $1-\log_{ 6 }({ 7 })$

$\begin{align*}&x=\frac{ 13 }{ 1-\log_{ 6 }({ 7 }) } \\&x\approx-151.10458\end{align*}$