Problem 16 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identifying elements in Exponential form

Identify the base, the exponent and the result in the equation. In this case, the base is \(15\), the exponent is \(2\) and the result is \(x\)

Step 2: Convert to Logarithmic form

The logarithmic form of the equation follows the pattern 'The logarithm to the base \(b\) of \(x\) is \(p\'\). This can be written as \(\log_b x = p\). Substitute \(b = 15, p = 2\) and \(x = x\) into this equation

Step 3: Writing the final Logarithmic form

After substitution, we get \(\log_{15} x = 2\)