Problem 15
Question
In Exercises \(1-40,\) 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 \( \log_b x^3 \) is \( 3 \log_b x \).
1Step 1: Identify the Expression
We need to evaluate or simplify: \(\log _{b} x^{3}\).
2Step 2: Apply Order of Operations
Following the order of operations (PEMDAS/BODMAS), we simplify the expression step by step, handling parentheses, exponents, multiplication/division, then addition/subtraction.
3Step 3: Compute the Result
Carrying out the operations systematically, we arrive at the result.
4Step 4: State the Result
The expanded form of \( \log_b x^3 \) is \( 3 \log_b x \).
Other exercises in this chapter
Problem 14
Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approxi
View solution Problem 14
Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(g(x)=\left(\frac{4}{3}\right)^{x
View solution Problem 15
Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approxi
View solution Problem 15
Write each equation in its equivalent logarithmic form. $$13^{2}=x$$
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