Problem

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

Solution

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}

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