Answer
a) $\dfrac{\log19}{\log3}$
b) $\dfrac{\ln19}{\ln3}$
c) $2.6801$
Work Step by Step
Using $\log_ba=\dfrac{\log_xa}{\log_xb}$ or the Change-of-Base Formula, the given expression, $
\log_3 19
$, is equivalent to
\begin{align*}
\text{a) using common logarithms: }
&
\dfrac{\log_{10}19}{\log_{10}3}
\\\\&=
\dfrac{\log19}{\log3}
\\\\
\text{b) using natural logarithms: }
&
\dfrac{\log_e19}{\log_e3}
\\\\&=
\dfrac{\ln19}{\ln3}
\\\\
\text{c) approximate value: }
&
2.6801
.\end{align*}
