Evaluating logarithmic expressions

Evaluate each expression.
(a) $\log _{7} \frac{1}{49}=\square$
(b) $\log _{3} 81=$

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Answer

\boxed{4}

Steps

Step 1 ：To solve this, we need to find the power to which 7 must be raised to get 1/49.

Step 2 ：We know that $7^2 = 49$, so $7^{-2} = 1/49$.

Step 3 ：$\log _{7} \frac{1}{49} = -2$

Step 4 ：\boxed{-2}

Step 5 ：To solve this, we need to find the power to which 3 must be raised to get 81.

Step 6 ：We know that $3^4 = 81$.

Step 7 ：$\log _{3} 81 = 4$

Step 8 ：\boxed{4}