Find the value of $x$ such that $2^x=10$ 
Given that $\log 5 = 0.7$ (to one decimal place), find the value of $x$ such that $2^x = 10$ (again to one decimal place)

I don't know what to do with the information that $10^{0.7} = 5$. Why is this information useful?

$2^x=10/\cdot \log_{10}$
$\log_{10}{2^x}=\log_{10}{10}$
$x\log_{10}{2}=1$
$x=\frac{1}{\log_{10}{2}}=\frac{1}{\log_{10}{\frac{10}{5}}}=\frac{1}{\log_{10}10-\log_{10}5}=\frac{1}{1-\log_{10}5}=\frac{1}{1-0.7}=\frac{1}{0.3}=\frac{1}{\frac{3}{10}}=\frac{10}{3}$
$x=\frac{10}{3}$
