Question

How does the value of log Subscript 2 Baseline 100 compare with the value of Log Subscript 6 Baseline 20?

Answer 1

Answer:

A.

Step-by-step explanation:

Answer 2

Answer:

• The value of   $\log_2 100$   is about 4 times the value of    $\log_6 20$

Explanation:

1. Change of base rule

       $\log_ab=\dfrac{\log_{10}b}{\log_{10}a}=\dfrac{\log b}{\log a}$

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

       $\log_2 100=\dfrac{\log 100}{\log 2}\approx 6.64$

       $\log_6 20=\dfrac{\log 20}{\log 6}\approx 1.67$

3.Compare

          $\dfrac{6.64}{1.67}\approx 3.97\approx 4$

4. Conclusion

The value   $\log_2 100$   is about 4 times the value of   $\log_6 20$