# How do you solve 2* 3^x = 7* 5^x?

##### 1 Answer
Jul 19, 2015

I found: $x = - 7.0421$

#### Explanation:

Try rearranging it: as:
${3}^{x} / {5}^{x} = \frac{7}{2}$
write it as:
${\left(\frac{3}{5}\right)}^{x} = \frac{7}{2}$
use the definition of logarithm to write:
${\log}_{\frac{3}{5}} \left(\frac{7}{2}\right) = x$
We can now use the change of base formula to transform our log into a quocient of natural logs (these can be evaluated using a pocket calculator) as:
$x = \frac{\ln \left(\frac{7}{2}\right)}{\ln \left(\frac{3}{5}\right)} = - 7.0421$