# How do you solve \log ( x + 19) = 2?

Jun 24, 2017

x = 81

#### Explanation:

When no base is written, it's assumed that the base is 10 .

$\log \left(x + 19\right) = 2$
${\log}_{10} \left(x + 19\right) = 2$

A general rule for logs is that if ${\log}_{b} \left(a\right) = c$, then ${b}^{c} = a$.

Therefore, we know that

${\log}_{10} \left(x + 19\right) = 2$
${10}^{2} = x + 19$

To find x, simplify the equation.

$100 = x + 19$
$81 = x$

Hope this helps!