Problem 1
Question
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{5}(7 \cdot 3)$$
Step-by-Step Solution
Verified Answer
\(\log_5 (7*3) = \log_5 7 + \log_5 3\)
1Step 1: Apply Product Rule of Logarithm
By applying the product rule of logarithm to the expression \(\log_5 (7*3)\), it can be rewritten as the sum of the logarithms of the factors. That is, \(\log_5 (7*3) = \log_5 7 + \log_5 3\).
2Step 2: Evaluate Logarithms
The expressions \(\log_5 7\) and \(\log_5 3\) cannot be simplified further since 7 and 3 are prime numbers, and their logarithms to the base 5 cannot be expressed with simple numbers. Therefore, the simplified expression is: \(\log_5 7 + \log_5 3\)
Other exercises in this chapter
Problem 1
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{x}=64$$
View solution Problem 1
Write each equation in its equivalent exponential form. $$4=\log _{2} 16$$
View solution Problem 1
Approximate each number using \(a\) calculator. Round your answer to three decimal places. $$ 2^{3.4} $$
View solution Problem 2
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{x}=81$$
View solution