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.

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Nightowl0 Nightowl0 · Answer 1 · 2017-02-09T16:17:24+01:00

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

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tardymanchester tardymanchester · Answer 2 · 2019-03-25T06:01:11+01:00

Answer:

[tex]\log_5 92=2.809[/tex]

[tex]\log_3 2.809=0.940[/tex]

Step-by-step explanation:

To find : Use the Change of Base Formula to evaluate [tex]\log_5 92[/tex].

Then convert [tex]\log_5 92[/tex] to a logarithm in base 3.

Solution :

Change of Base Formula,

[tex]\log_b x=\frac{log_a x}{\log_a b}[/tex]

Applying this,

[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]

Now, converting [tex]\log_5 92[/tex] to a logarithm in base 3

[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]