Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[a=\log_{10}{4}\]
Use Change of Base Rule: \(\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}\).
\[a=\frac{\log{4}}{\log{10}}\]
Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\)\(\log{4}\) -> \(\log{{2}^{2}}\) -> \(2\log{2}\).
\[a=\frac{2\log{2}}{\log{10}}\]
Use Rule of Ten: \(\log{10}=1\).
\[a=\frac{2\log{2}}{1}\]
Simplify \(\frac{2\log{2}}{1}\) to \((2\log{2})\).
\[a=2\log{2}\]
Decimal Form: 0.602060
a=2*log(2)
