# How do you solve the exponential equation 9^x=3^(x+27)?

We have that

${9}^{x} = {3}^{x + 27}$

${3}^{2 x} = {3}^{x} \cdot {3}^{27}$

${3}^{2 x} / {3}^{x} = \frac{{3}^{x} \cdot {3}^{27}}{3} ^ x$

${3}^{x} = {3}^{27}$

$x = 27$

Mar 5, 2017

color(red)(x=27

#### Explanation:

${9}^{x} = {3}^{x + 27}$

${3}^{2 x} = {3}^{x + 27}$

multiplyL.H.S. and R.H.S. by color(red)(1/3

$\frac{\textcolor{red}{1}}{\cancel{\textcolor{red}{3}}} \times {\cancel{\textcolor{red}{3}}}^{2 x} / \textcolor{red}{1} = \frac{{\cancel{\textcolor{red}{3}}}^{x + 27}}{\textcolor{red}{1}} \times \frac{\textcolor{red}{1}}{\cancel{\textcolor{red}{3}}}$

$2 x = x + 27$

$2 x - x = 27$

color(red)(x=27