Given the following question:
Which equation is equivalent to logx 36 = 2
[tex]\begin{gathered} \log _x36=2 \\ \frac{1}{\log_{36}\left(x\right)}=2 \\ \frac{1}{\log_{36}\left(x\right)}\log _{36}\mleft(x\mright)=2\log _{36}\mleft(x\mright) \\ 1=2\log _{36}\mleft(x\mright) \\ 2\log _{36}\mleft(x\mright)=1 \\ \log _{36}\mleft(x\mright)=\frac{1}{2}=6 \\ =6 \end{gathered}[/tex]
Now we have to find the option that also equals 6:
Starting with Option B:
[tex]\begin{gathered} x^2=36 \\ x=\sqrt{36},\: x=-\sqrt{36} \\ 6\times6=36 \\ \sqrt[]{-36}=-6 \\ \text{Solutions} \\ x=6 \\ x=-6 \end{gathered}[/tex]
Your answer is option B.
