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: Understand the definition of a logarithm
A logarithm is the exponent to which the base must be raised to obtain the number. So, the logarithm of the number \( 16 \) in base \( 4 \) is intended to find the exponent 'x' that satisfies the equation \( 4^{x} = 16 \)
2Step 2: Use the properties of logarithms
We know that \( 4^2 = 16 \). This translates to '2' is the exponent we need to raise \( 4 \) to in order to get \( 16 \)
3Step 3: Find the value of the logarithm
Therefore, \( \log _{4} 16 = 2 \)
Other exercises in this chapter
Problem 20
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution Problem 21
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$e^{x+1}=\frac{1}{e}$$
View solution Problem 21
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution Problem 22
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$e^{x+4}=\frac{1}{e^{2 x}}$$
View solution