# How do you solve -5*10^(3b)=-77?

Sep 5, 2016

$b = \frac{1}{3} \left(\log \left(77\right) - \log \left(5\right)\right)$

#### Explanation:

We have: $- 5 \cdot {10}^{3 b} = - 77$

Let's begin by dividing both sides of the equation by $- 5$:

$\implies {10}^{3 b} = \frac{77}{5}$

Then, let's apply logarithms to both sides:

$\implies \log \left({10}^{3 b}\right) = \log \left(\frac{77}{5}\right)$

Now, using the laws of logarithms:

$\implies 3 b \log \left(10\right) = \log \left(77\right) - \log \left(5\right)$

$\implies 3 b = \log \left(77\right) - \log \left(5\right)$

$\implies b = \frac{1}{3} \left(\log \left(77\right) - \log \left(5\right)\right)$