# How do you solve -4*3^(5x)-4=-30?

Apr 20, 2018

$\textcolor{b l u e}{x = \ln \frac{\frac{13}{2}}{5 \ln \left(3\right)} \approx 0.3407575530}$

#### Explanation:

$- 4 \cdot {3}^{5 x} - 4 = - 30$

$- 4 \cdot {3}^{5 x} = - 26$

Multiply by $- 1$:

$4 \cdot {3}^{5 x} = 26$

Divide by 4:

${3}^{5 x} = \frac{13}{2}$

Taking natural logarithms of both sides:

$5 x \ln \left(3\right) = \ln \left(\frac{13}{2}\right)$

Divide by $5 \ln \left(3\right)$:

$x = \ln \frac{\frac{13}{2}}{5 \ln \left(3\right)} \approx 0.3407575530$