Problem 15
Question
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b} x^{3}$$
Step-by-Step Solution
Verified Answer
The expanded form of the logarithmic expression \(\log _{b} x^{3}\) is \(3 \log _{b} x\).
1Step 1: Identify the Expression
We expand the logarithmic expression:
Use properties of logarithms to expand each logarithmic expression as much as
possible. Where possible, evaluate logarithmic expressions without using a
calculator.
$$\log _{b} x^{3}$$
Use properties of logarithms to expand each logarithmic expression as much as
possible. Where possible, evaluate logarithmic expressions without using a
calculator.
$$\log _{b} x^{3}$$
2Step 2: Apply Logarithm Rules
- Product Rule: \(\log_b(MN) = \log_b(M) + \log_b(N)\)
- Quotient Rule: \(\log_b(M/N) = \log_b(M) - \log_b(N)\)
- Power Rule: \(\log_b(M^p) = p\log_b(M)\)
3Step 3: Expanded Expression
The expanded form of the logarithmic expression \(\log _{b} x^{3}\) is \(3 \log _{b} x\).
Other exercises in this chapter
Problem 14
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calcula
View solution Problem 15
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$6^{\frac{x-3}{4}}=\sqrt{6}$$
View solution 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