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

`\log_5 92=2.809`

`\log_3 2.809=0.940`

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=(log_a x)/(\log_a b)`

Applying this,

`\log_5 92=(log 92)/(\log 5)`

`\log_5 92=(1.963)/(0.698)`

`\log_5 92=2.809`

Now, converting
`\log_5 92` to a logarithm in base 3

`\log_3 2.809=(log 2.809)/(\log 3)`

`\log_3 2.809=(0.448)/(0.477)`

`\log_3 2.809=0.940`

Therefore, The solution is
`\log_3 2.809=0.940`