How does the value of log Subscript 2 Baseline 100 compare with the value of Log Subscript 6 Baseline 20?
The value of Log Subscript 2 Baseline 100 is about 4 times the value of Log Subscript 6 Baseline 20.
The value of Log Subscript 2 Baseline 100 is about One-fourth times the value of Log Subscript 6 Baseline 20.
The value of Log Subscript 2 Baseline 100 is about 3 times the value of Log Subscript 6 Baseline 20.
The value of Log Subscript 2 Baseline 100 is about One-third times the value of Log Subscript 6 Baseline 20.

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Edufirst Edufirst · Answer 1 · 2020-03-17T10:08:54+01:00

Answer:

The value of [tex]\log_2 100[/tex] is about 4 times the value of [tex]\log_6 20[/tex]

Explanation:

1. Change of base rule

[tex]\log_ab=\dfrac{\log_{10}b}{\log_{10}a}=\dfrac{\log b}{\log a}[/tex]

2. Apply change of base rule to each of the given logarithm

[tex]\log_2 100=\dfrac{\log 100}{\log 2}\approx 6.64[/tex]

[tex]\log_6 20=\dfrac{\log 20}{\log 6}\approx 1.67[/tex]

3.Compare

[tex]\dfrac{6.64}{1.67}\approx 3.97\approx 4[/tex]

4. Conclusion

The value [tex]\log_2 100[/tex] is about 4 times the value of [tex]\log_6 20[/tex]

MrRoyal MrRoyal · Answer 2 · 2022-01-19T13:25:16+01:00

The value of [tex]\log_2(100)[/tex] is about 4 times the value of [tex]\log_6(20)[/tex].

Logarithmic expressions are the inverse or opposite functions to exponentiation

The logarithmic expressions are given as:

[tex]\log_2(100)[/tex] and [tex]\log_6(20)[/tex]

Start by evaluating both logarithmic expressions.

Using a calculator, we have:

[tex]\log_2(100) = 6.64[/tex]

[tex]\log_6(20) = 1.67[/tex]

Divide both equations

[tex]\frac{\log_2(100)}{\log_6(20)} = \frac{6.64}{1.67}[/tex]

Simplify the fraction

[tex]\frac{\log_2(100)}{\log_6(20)} = 3.97[/tex]

Approximate

[tex]\frac{\log_2(100)}{\log_6(20)} \approx 4[/tex]

This means that,

The value of [tex]\log_2(100)[/tex] is about 4 times the value of [tex]\log_6(20)[/tex].