# How do you solve 10^(x+2) - 12 = 22  and find any extraneous solutions?

Jul 22, 2016

The Soln. is $x = - 0.4685$

#### Explanation:

${10}^{x + 2} - 12 = 22 \Rightarrow {10}^{x + 2} = 12 + 22 = 34$

$\Rightarrow {\log}_{10} {10}^{x + 2} = {\log}_{10} 34$

$\Rightarrow \left(x + 2\right) {\log}_{10} 10 = 1.5315$..................[Using LogTable]

$\Rightarrow \left(x + 2\right) \cdot 1 = 1.5315$

$\Rightarrow x + 2 = 1.5315$

$\Rightarrow x = 1.5315 - 2$

$\Rightarrow x = - 0.4685$ is the Soln.