# How do you solve 3(5)^(2x−3) = 6?

##### 1 Answer
Apr 3, 2018

$x = \ln \frac{250}{\ln} \left(25\right)$

#### Explanation:

Isolate the exponential ${5}^{2 x - 3}$ by dividing both sides by $3 ,$ yielding

${5}^{2 x - 3} = 2$

Furthermore, recall that ${x}^{a - b} = {x}^{a} / {x}^{b} ,$ so ${5}^{2 x - 3} = {5}^{2 x} / {5}^{3} = {5}^{2 x} / 125$

${5}^{2 x} / 125 = 2$

${5}^{2 x} = 250$

Now, apply the natural logarithm to both sides.

$\ln \left({5}^{2 x}\right) = \ln \left(250\right)$

Recall that $\ln \left({a}^{b}\right) = b \ln a ,$ so $\ln \left({5}^{2 x}\right) = 2 x \ln \left(5\right)$

$2 x \ln \left(5\right) = \ln \left(250\right)$

Now, solve for $x .$ This will be much simpler now as it is not in an exponent or logarithm.

$2 x = \ln \frac{250}{\ln} \left(5\right)$

$x = \ln \frac{250}{2 \ln 5}$

$x = \ln \frac{250}{\ln} \left(25\right)$ as $2 \ln 5 = \ln \left({5}^{2}\right) = \ln \left(25\right)$