Problem 36
Question
Evaluate each expression without using a calculator. $$\log _{4} 4^{6}$$
Step-by-Step Solution
Verified Answer
The value of \( \log _{4} 4^{6} \) is 6.
1Step 1: Identify the base and the exponent
In the expression \(\log _{4} 4^{6}\), the base is 4 and the exponent is 6. This matches the structure of the logarithm property \(\log_b b^x = x\).
2Step 2: Apply the logarithm property
By applying property \(\log_b b^x = x\), we can simplify \(\log _{4} 4^{6}\) to 6.
Other exercises in this chapter
Problem 36
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions
View solution Problem 36
How can you tell if an exponential model describes exponential growth or exponential decay?
View solution Problem 36
Graph functions \(f\) and \(g\) in the same rectangular coordinate system. If applicable, use a graphing utility to confirm your hand-drawn graphs. \(f(x)=3^{x}
View solution Problem 37
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions
View solution