Given:
[tex]\log _{\sqrt[]{3}}20[/tex]
The change of base formula states that,
[tex]\log _bx=\frac{\log _cx}{\log _cb}[/tex]
For the given expression,
[tex]\begin{gathered} \log _{\sqrt[]{3}}20=\frac{\log_{10}20}{\log_{10}\sqrt[]{3}} \\ =\frac{\log_{10}20}{\frac{1}{2}\log_{10}3} \\ =\frac{2\log_{10}20}{\log_{10}3} \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} \log _{\sqrt[]{3}}20=\frac{\log_{10}20}{\log_{10}\sqrt[]{3}} \\ or\text{ in simplified form,} \\ \log _{\sqrt[]{3}}20=\frac{2\log_{10}20}{\log_{10}3} \end{gathered}[/tex]
