# How do you solve log x^2+1=5?

Mar 21, 2016

$x = 100$

#### Explanation:

$\log {x}^{2} + 1 = 5$
$\log {x}^{2} = 4$-> subtract 1 from both sides
$2 \log x = 4$->Use property ${\log}_{b} {x}^{n} = n \cdot {\log}_{b} x$
$\log x = 2$-> divide both sides by 2
${10}^{2} = x$->use property $y = {\log}_{b} x \iff {b}^{y} = x$
$x = 100$