How do you solve the exponential equation 3^(x-7)=27^(2x)?

Feb 19, 2017

$x = - \frac{7}{5}$

Explanation:

Rewrite the right hand side as follows

${3}^{x - 7} = {\left({3}^{3}\right)}^{2 x}$

Using the property ${\left({a}^{y}\right)}^{x} = {a}^{y x}$

We can further rewrite the right side

${3}^{x - 7} = {3}^{6 x}$

Since we now have both sides in terms of the same base

$x - 7 = 6 x$

$- 5 x = 7$

$x = - \frac{7}{5}$