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Chapter 4: Problem 16

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

Short Answer

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

Step by step solution

01

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 \(x\).
02

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 \( \log_{15}x = 2 \).

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