Problem 5 - College Algebra

Question

Write each equation in its equivalent exponential form. $$5=\log _{b} 32$$

Step-by-Step Solution

Answer

The equation \(5=log_b 32\) in its equivalent exponential form is \(b^5 = 32\).

Step 1: Identify the base, exponent and result

In the logarithm expression, \(5=log_b 32\), the base is \(b\), the exponent is \(5\) (because in logarithmic form, the number after log is the exponent), and the result is \(32\).

Step 2: Apply the Conversion Rule

Convert the logarithmic equation into exponential form using the rule that if \(y = log_b x\), then it is the same as \(b^y = x\). Therefore, the exponential form of the given equation will be \(b^5 = 32\).