# How do you solve 3-log 7x + 4 = 5?

Dec 2, 2015

Use the exponential function and a property of logarithms to find that
$x = {e}^{2} / 7$

#### Explanation:

We will be using the property that

${e}^{\log} \left(a\right) = a$

$3 - \log \left(7 x\right) + 4 = 5$

$\implies - \log \left(7 x\right) = 5 - 3 - 4 = - 2$

$\implies \log \left(7 x\right) = 2$

$\implies {e}^{\log} \left(7 x\right) = {e}^{2}$

$\implies 7 x = {e}^{2}$$\text{ }$ (by the above property)

$\implies x = {e}^{2} / 7$