Problem 40 - College Algebra

Question

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

Step-by-Step Solution

Answer

The value of the expression \(\log _{4} 4^{6}\) is 6.

Step 1: Identify the Logarithm's Base and Exponent

First, identify the base and the exponent in the logarithm. Here, the base of the logarithm is 4 and the exponent is 6.

Step 2: Apply the basic property of logarithms

The basic property of logarithms states that if \(\log_b b^x = x\). This means any base with its log will just equal to the power it is raised to.

Step 3: Evaluate the equation

Substituting b=4 and x=6 into the property of logarithms equation, we get \(\log _{4} 4^{6} = 6 \).