Problem 5
Question
Write each equation in its equivalent exponential form. $$5=\log _{b} 32$$
Step-by-Step Solution
Verified Answer
The equivalent exponential form of the given equation is \(b^5 = 32\).
1Step 1: Recognize the base, exponent and result of the logarithm
Observe that in the given logarithmic equation \(5 = \log_b 32\), the base of the logarithm is 'b', the result of the logarithm is 5, and the number we are taking the log of is 32.
2Step 2: Write down the exponential form
According to the definition of the logarithm, the base 'b' raised to the power of the result gives the number, i.e. if \(5 = \log_b 32\), then the equivalent exponential form is \(b^5 = 32\).
Other exercises in this chapter
Problem 5
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{2 x-1}=32$$
View solution Problem 5
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution Problem 5
Approximate each number using a calculator. Round your answer to three decimal places. $$4^{-1.5}$$
View solution Problem 6
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{2 x+1}=27$$
View solution