Question

(Evaluate each logarithm. Use the change of base formula when necessary) helpppp y’all

Answer 1

The value of $\log _{6}(36)$ is 2.

Solution:

Given expression is $\log _{6}(36)$.

To evaluate the expression:

$\log _{6}(36)$

36 can be written as 6².

       $=\log _{6}\left(6^{2}\right)$

Using log rule: $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$

       $=2 \log _{6}(6)$

Using log rule: $\log _{a}(a)=1$ so that $\log _{6}(6)=1$

       = 2(1)

       = 2

$\log _{6}(36)=2$

Hence the value of $\log _{6}(36)$ is 2.