Problem 21
Question
Evaluate each expression without using a calculator. $$\log _{4} 16$$
Step-by-Step Solution
Verified Answer
The value of \(\log _{4} 16\) is 2.
1Step 1: Determine the Base and Argument of Logarithm
The logarithm given is \(\log _{4} 16\). In this case, the base of the logarithm is 4, and the argument is 16.
2Step 2: Find the Exponent
You need to solve for \(x\) in the equation \(4^x = 16\). This is essentially what \(\log _{4} 16\) means: what power \(x\) do you need to raise 4 to, to get 16. Here, \(x = 2\) because \(4^2 = 16\).
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