Question

category: homework current score: 26.8/43 points current learning objective: evaluating logarithms question 34 practice similar questions score: 0 of 1 point evaluate the logarithm without using a calculator. \\(\log_{4}(64) =\\) enter your answer \\(\sqrt{x}\\)

Explanation:

Step1: Recall the logarithm definition

Let \(y = \log_{4}(64)\). By the definition of logarithms, if \(y=\log_{a}(x)\), then \(a^{y}=x\). So for \(y = \log_{4}(64)\), we have \(4^{y}=64\).

Step2: Express 64 as a power of 4

We know that \(4 = 2^{2}\) and \(64=2^{6}\). Also, \(4^{3}=(2^{2})^{3}=2^{6}\). So \(4^{3}=64\).

Answer:

\(3\)