Problem 16 - College Algebra Essentials

Question

Write each equation in its equivalent logarithmic form. $$15^{2}=x$$

Step-by-Step Solution

Answer

The equivalent logarithmic form of the given exponential equation \(15^{2} = x \) is \( \log_{15}x = 2 \).

Step 1: Identify the Base, Exponent, and Result

In the given exponential equation \(15^{2} = x \), the base is 15, the exponent is 2 and the result is \(x\).

Step 2: Convert the Exponential Form to Logarithmic Form

Now, apply the relationship between exponential and logarithmic forms: For an equation \( b^{y} = x \), its equivalent logarithmic form is \( \log_{b}x = y \). Therefore, converting the exponential form \(15^{2} = x \) to its equivalent logarithmic form gives \( \log_{15}x = 2 \).