9514 1404 393
Answer:
x = -9 (as you know)
Step-by-step explanation:
[tex]\log_6\dfrac{1}{6}=\dfrac{x}{9}\\\\\log_6{(6^{-1})}=\dfrac{x}{9}\\\\-1=\dfrac{x}{9}\\\\x=(-1)(9)=\boxed{-9}[/tex]
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I find it helpful to remember that a logarithm is an exponent.
[tex]\log_a(a^b)=b[/tex]
