# If 5^(3x)=8, find 5^(3+x)?

Jun 8, 2017

${5}^{3 + \frac{\ln \left(8\right)}{3 \ln \left(3\right)}}$

#### Explanation:

We have: ${5}^{3 x} = 8$

Let's apply $\ln$ to both sides of the equation:

$R i g h t a r r o w \ln \left({5}^{3 x}\right) = \ln \left(8\right)$

Using the laws of logarithms:

$R i g h t a r r o w 3 x \ln \left(5\right) = \ln \left(8\right)$

$R i g h t a r r o w 3 x = \frac{\ln \left(8\right)}{\ln \left(3\right)}$

$\therefore x = \frac{\ln \left(8\right)}{3 \ln \left(3\right)}$

Now, let's evaluate ${5}^{3 + x}$:

$R i g h t a r r o w {5}^{3 + x} = {5}^{3} \cdot {5}^{x}$

$\therefore {5}^{3 + x} = {5}^{3 + \frac{\ln \left(8\right)}{3 \ln \left(3\right)}}$