Problem 16
Question
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b} x^{7}$$
Step-by-Step Solution
Verified Answer
The expanded expression of \( \log_b x^{7} \) is \( 7 \cdot \log_b x \)
1Step 1: Identify Logarithmic Property
Recognize the needed logarithmic property, which states that \( \log_b a^m = m * \log_b a \). This means you can take the exponent (7 in this case) and move it to the front of the logarithmic expression as a multiplier.
2Step 2: Apply the Property
Apply this property to the given logarithmic expression to get \( 7 \cdot \log_b x \)
Other exercises in this chapter
Problem 15
Write each equation in its equivalent logarithmic form. $$13^{2}=x$$
View solution Problem 16
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$7^{\frac{x-2}{6}}=\sqrt{7}$$
View solution Problem 16
Write each equation in its equivalent logarithmic form. $$15^{2}=x$$
View solution Problem 17
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$4^{x}=\frac{1}{\sqrt{2}}$$
View solution