Answer:
\(\log_5 92=2.809\)
\(\log_3 2.809=0.940\)
Step-by-step explanation:
Given : Expression \(\log_5 92\)
To find : Use the Change of Base Formula to evaluate the expression also convert the expression to a logarithm in base 3?
Solution :
Applying the change of Base Formula,
i.e. \(\log_b x=\frac{log_a x}{\log_a b}\)
We get,
\(\log_5 92=\frac{\log 92}{\log 5}\)
\(\log_5 92=\frac{1.963}{0.698}\)
\(\log_5 92=2.809\)
So, The expression is \(\log_5 92=2.809\)
Now, converting the expression to a logarithm in base 3.
Taking log base 3 in 2.809,
\(\log_3 2.809=\frac{log 2.809}{\log 3}\)
\(\log_3 2.809=\frac{0.448}{0.477}\)
\(\log_3 2.809=0.940\)
Therefore, The solution is \(\log_3 2.809=0.940\)
