Question

Use the Change of Base Formula to evaluate log5 92. Then convert log5 92 to a logarithm in base 3. Round to the nearest thousandth.

Answer 1

I was thinking that the answer  could be 

2.810; log3 21.903
         
            OR


 2.810; log3 55.2 

So, log5 of 92 is between 2.5 and 3  Correct answer is A

Answer 2

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 $\log_3 2.809=0.940$