Question

How does the value of log2^100 compare with the value of log6^20?
A. Value of log2^100 is about 4 times the value of log6^20
B. Value of log2^100 is about 1/4 times the value of log6^20
C. Value of log2^100 is about 3 times the value of log6^20
D. Value of log2^100 is about 1/3 times the value of log6^20

Answer 1

We are given

First value is :

$log_2(100)$

we can simplify it

we can use base change formula

$log_2 (100)=\frac{ln\left(100\right)}{ln\left(2\right)}$

$log_2 (100)=6.643856$

Second value is :

$log_6(20)$

we can simplify it

we can use base change formula

$log_6(20)=\frac{ln\left(20\right)}{ln\left(6\right)}$

$log_6(20)=1.67195$

so, we know that

6.6438 is almost 4 times of 1.67195

so, option-A.........Answer

Answer 2

Value of log2^100 compare with the value of log6^20 id related as the value of log2^100 is about 4 times the value of log6^20. The option A is correct.

What is exponent of log rule?

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

The first function of log is given with base 2.

$\log_2(100)$

The second function of log is given with base 6.

$\log_6(100)$

To compare the value of both the log function, find out the value of them.

Using the base change formula of logarithmic function we can write the first function as,

$\log_2(100)=\dfrac{\log(100)}{\log(2)}\\\log_2(100)=6.643856$

Let the above equation is equation 1.

Using the base change formula of logarithmic function we can write the second function as,

$\log_6(20)=\dfrac{\log(20)}{\log(6)}\\\log_6(20)=1.67195\\\log_6(20)=1.67195\times\dfrac{4}{4}\\\log_6(20)=6.643856\times\dfrac{1}{4}$

Comparing the above equation with equation 4 we get that the value of log2^100 is about 4 times the value of log6^20

Hence, the option A is the correct option.

Learn more about the rules of logarithmic function here;

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