The value of [tex]\log _{6}(36)[/tex] is 2.
Solution:
Given expression is [tex]\log _{6}(36)[/tex].
To evaluate the expression:
[tex]\log _{6}(36)[/tex]
36 can be written as 6².
[tex]=\log _{6}\left(6^{2}\right)[/tex]
Using log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]
[tex]=2 \log _{6}(6)[/tex]
Using log rule: [tex]\log _{a}(a)=1[/tex] so that [tex]\log _{6}(6)=1[/tex]
= 2(1)
= 2
[tex]\log _{6}(36)=2[/tex]
Hence the value of [tex]\log _{6}(36)[/tex] is 2.
