# How do you solve 3.1^(a-3)=9.42?

Oct 21, 2016

$a = 4.9824$

#### Explanation:

As ${3.1}^{a - 3} = 9.42$, taking logarithm of both sides to base $10$, we get

$\left(a - 3\right) \times \log 3.1 = \log 9.42$ and

$\left(a - 3\right) = \log \frac{9.42}{\log} 3.1 = \frac{0.97405}{0.49136} = 1.9824$

and $a = 1.9824 + 3 = 4.9824$