Note the change of base rule below
[tex]\log _ab=\frac{\log _cb}{\log _ca}[/tex]The given logarithmic expression is:
[tex]\log _{13}21[/tex]Applying the change of base rule
[tex]\log _{13}21=\frac{\log _{10}21}{\log _{10}13}[/tex]Note that:
[tex]\begin{gathered} \log _{10}21=1.3222 \\ \log _{10}13=1.1139 \end{gathered}[/tex]The evaluation therefore becomes:
[tex]\begin{gathered} \log _{13}21=\frac{1.3222}{1.1139} \\ \log _{13}21=1.187 \end{gathered}[/tex]