004 Sample Final A, Problem 19

Solve for x:      $\log _{6}{\frac {1}{36}}=x$

Foundations
How do we remove logs from an equation?
Answer:
The definition of the logarithm tells us that if $\log _{6}(x)=y$, then $6^{y}=x$.

Solution:

Step 1:
By the definition of the logarithm, $\log _{6}{\frac {1}{36}}=x$ means $6^{x}={\frac {1}{36}}$.

Step 2:
Now, we can solve for $x$. Since $6^{x}={\frac {1}{36}}$,
we must have $x=-2$.

Final Answer:
$x=-2$

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