Problem 3 - College Algebra

Question

Write each equation in its equivalent exponential form. $$2=\log _{3} x$$

Step-by-Step Solution

Answer

The equivalent exponential form of the equation \(2=\log _{3} x\) is \(3^2=x\).

Step 1: Understanding Logarithmic Notation

In the given logarithmic equation \(2=\log _{3} x\), '3' is the base, 'x' is the argument (or 'number') of the log, and '2' is the log (or 'exponent').

Step 2: Conversion to Exponential Form

The rule for converting log form to exponential form is 'base to the log equals the number'. So, the base is 3, the exponent is 2 (the given log), and the number that results is 'x' (from one side of our equation). This can be expressed as \(3^2=x\).