Answer:
[tex]\log_5 92=2.809[/tex]
[tex]\log_3 2.809=0.940[/tex]
Step-by-step explanation:
Given : Expression [tex]\log_5 92[/tex]
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. [tex]\log_b x=\frac{log_a x}{\log_a b}[/tex]
We get,
[tex]\log_5 92=\frac{\log 92}{\log 5}[/tex]
[tex]\log_5 92=\frac{1.963}{0.698}[/tex]
[tex]\log_5 92=2.809[/tex]
So, The expression is [tex]\log_5 92=2.809[/tex]
Now, converting the expression to a logarithm in base 3.
Taking log base 3 in 2.809,
[tex]\log_3 2.809=\frac{log 2.809}{\log 3}[/tex]
[tex]\log_3 2.809=\frac{0.448}{0.477}[/tex]
[tex]\log_3 2.809=0.940[/tex]
Therefore, The solution is [tex]\log_3 2.809=0.940[/tex]
