Answer:
[tex]-2[/tex]
Step-by-step explanation:
[tex]\frac{\log _{10}\left(\frac{1}{36}\right)}{\log _{10}\left(6\right)}[/tex]
[tex]\log _6\left(\frac{1}{36}\right)[/tex]
[tex]-\log _6\left(36\right)[/tex]
[tex]-\log _6\left(6^2\right)[/tex]
[tex]-2\log _6\left(6\right)[/tex]
[tex]-2\cdot \:1[/tex]
[tex]-2[/tex]