# How do you solve 2^x = 10?

${a}^{b} = c \implies {\log}_{a} \left(c\right) = b$
${2}^{x} = 10 \implies {\log}_{2} \left(10\right) = x \implies x = {\log}_{2} \left(2 \cdot 5\right) \implies x = {\log}_{2} \left(2\right) + {\log}_{2} \left(5\right)$
$\implies x = 1 + {\log}_{2} \left(5\right)$
$x = 1 + 2.32 = \underline{3.32}$