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Use the change of base formula to evaluate the expression.log subscript 13 21=

Use The Change Of Base Formula To Evaluate The Expressionlog Subscript 13 21 class=

Sagot :

Answer:[tex]\log _{13}21=1.187[/tex]Explanation:

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]