Answer:
\(\log_5 92=2.809\)
\(\log_3 2.809=0.940\)
Step-by-step explanation:
To find : Use the Change of Base Formula to evaluate \(\log_5 92\).
Then convert \(\log_5 92\) to a logarithm in base 3.
Solution :
Change of Base Formula,
\(\log_b x=\frac{log_a x}{\log_a b}\)
Applying this,
\(\log_5 92=\frac{log 92}{\log 5}\)
\(\log_5 92=\frac{1.963}{0.698}\)
\(\log_5 92=2.809\)
Now, converting \(\log_5 92\) to a logarithm in base 3
\(\log_3 2.809=\frac{log 2.809}{\log 3}\)
\(\log_3 2.809=\frac{0.448}{0.477}\)
\(\log_3 2.809=0.940\)
Therefore, The solution is \(\log_3 2.809=0.940\)
