Problem 20 - Introductory and Intermediate Algebra for College Students 4th

Question

Write each equation in its equivalent logarithmic form. $$8^{y}=300$$

Step-by-Step Solution

Answer

The logarithmic form of the given equation \(8^{y} = 300\) is \(\log_8 300 = y\).

Step 1: Identify the base, exponent and result in the given equation

The equation given is \(8^{y} = 300\). Here, 8 is the base, 'y' is the exponent and 300 is the result.

Step 2: Apply the conversion formula

Convert the given equation into its logarithmic form using the formula: if \(b^y = x\), then \(\log_b x = y\). Substituting the identified base, exponent and result, the equivalent logarithmic form of \(8^{y} = 300\) is \(\log_8 300 = y\).