Problem 4
Question
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{9}(9 x)$$
Step-by-Step Solution
Verified Answer
The expanded form of the logarithmic expression \( \log_{9} (9x) \) is \( 1 + \log_{9} (x) \).
1Step 1: Apply Logarithmic Properties
Firstly, rewrite the expression \( \log_{9} (9x) \) using the logarithmic property \( \log_b (bc) = \log_b (b) + \log_b (c) \). Therefore, \( \log_{9} (9x) \) can be rewritten as \( \log_{9} (9) + \log_{9} (x) \).
2Step 2: Simplify Logarithmic Expression
Secondly, simplify the expression \( \log_{9} (9) \) using the property \( \log_b (b) = 1 \). Since the base and argument are the same, \( \log_{9} (9) \) is equal to 1. Therefore, the expression is simplified as \( 1 + \log_{9} (x) \).
Other exercises in this chapter
Problem 3
Approximate each number using a calculator. Round your answer to three decimal places. $$3^{\sqrt{5}}$$
View solution Problem 4
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=625$$
View solution Problem 4
Write each equation in its equivalent exponential form. $$2=\log _{9} x$$
View solution Problem 4
Approximate each number using a calculator. Round your answer to three decimal places. $$5^{\sqrt{3}}$$
View solution