[tex]$\log _{2}\left(\frac{1}{16}\right)=-4[/tex]
Solution:
Given expression:
[tex]$\log _{2}\left(\frac{1}{16}\right)[/tex]
To solve this expression:
[tex]$\log _{2}\left(\frac{1}{16}\right)[/tex]
Using log rule: [tex]\log _{a}\left(\frac{1}{x}\right)=-\log _{a}(x)[/tex]
[tex]=-\log _{2}(16)[/tex]
16 can be written as [tex]2^4[/tex].
[tex]=-\log _{2}\left(2^{4}\right)[/tex]
Using log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex] so that [tex]\log _{2}\left(2^{4}\right)=4 \log _{2}(2)[/tex]
[tex]=-4 \log _{2}(2)[/tex]
Using log rule: [tex]\log _{a}(a)=1[/tex] so that [tex]\log _{2}(2)=1[/tex]
[tex]=-4 \cdot 1[/tex]
= –4
[tex]$\log _{2}\left(\frac{1}{16}\right)=-4[/tex]
