Problem 40 - College Algebra Essentials

Question

Evaluate each expression without using a calculator. $$\log _{4} 4^{6}$$

Step-by-Step Solution

Answer

The value of the expression is 6.

Step 1: Identify the problem.

The exercise is asking to evaluate the expression without using a calculator. The given expression is \(\log_4 4^6\).

Step 2: Apply the logarithmic rule.

To solve this expression, we can apply the logarithmic rule \(\log_b(b^x) = x\). Here, the base of the logarithm (\(b\)) is 4, and the exponent (\(x\)) is 6. Applying the rule gives us \(\log_4 4^6 = 6\).

Step 3: Write down the answer.

The expression \(\log_4 4^6\) simplifies to 6. This is the answer.