Problem 15 - College Algebra Essentials

Question

Write each equation in its equivalent logarithmic form. $$13^{2}=x$$

Step-by-Step Solution

Answer

The logarithmic form of the expression \(13^{2} = x\) is \(\log_{13}(x) = 2\).

Step 1: Identify the Base, Exponent and Result

In the given exponential expression \(13^{2} = x\), understand that '13' is the base, '2' is the exponent, and 'x' is the result.

Step 2: Convert to Logarithmic Form

Using the logarithmic conversion formula, \(b^{y} = z\) can be rewritten as \(\log_{b}(z) = y\). This simply means 'log base b of z equals y'. Thus the exponential equation \(13^{2} = x\) can be expressed in logarithmic form as \(\log_{13}(x) = 2\).