Problem 121 - College Algebra

Question

What question can be asked to help evaluate \(\log _{3} 81 ?\)

Step-by-Step Solution

Answer

The value of \(\log _{3} 81 \) is 4.

Step 1: Understanding Logarithms

The logarithm \(\log _{3} 81 \) can be represented as an exponentiation where the base is 3 and the result is 81. The exponent is what we're trying to find

Step 2: Breaking Down the Problem

The problem can be broken down into the equation \(3^x = 81\). Hence we need to find a value of 'x' which makes this equation true.

Step 3: Finding the Value

We know that \(3^4 = 81\). Therefore, in the equation \(3^x = 81\), 'x' must be 4.