## Algebra 2 Common Core

$x\approx0.830$
Taking the logarithm of both sides, the given equation, $4^{2x}=10 ,$ is equivalent to \begin{align*} \log4^{2x}=\log10 .\end{align*} Using the properties of logarithms, the equation above is equivalent to \begin{align*} \log4^{2x}&=1 &\left(\text{use }\log10=1 \right) \\ 2x\log4&=1 &\left(\text{use }\log_ba^x=x\log_ba \right) \\\\ \dfrac{2x\log4}{2\log4}&=\dfrac{1}{2\log4} \\\\ x&=\dfrac{1}{2\log4} \\\\ x&\approx0.830 .\end{align*} Hence, the solution is $x\approx0.830 .$