Problem 15 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify the base, exponent, and result

The base in the equation is 13, the exponent is 2, and the result of the operation is \(x\).

Step 2: Apply the logarithm definition

The definition of logarithm allows the rewriting of \(13^{2} = x\) into \(\log_{13}(x) = 2\). The base of the logarithm is the same as the base of the power in the original equation, and the argument of the logarithm is equal to what was the result of the power function.

Step 3: Final logarithmic form

The final form of the equivalent equation is therefore \(\log_{13}(x) = 2\). This form reads: 'The logarithm base 13 of \(x\) equals 2', which means the number \(x\) is the result of raising 13 the power of 2.