Solve the following logarithmic equation. \[ \log _{3} x=3 \]

To solve the logarithmic equation: \[ \log_{3} x = 3 \] **Step 1: Understand the Logarithmic Equation** The equation \(\log_{3} x = 3\) asks for the value of \(x\) such that when you take the logarithm of \(x\) with base \(3\), you get \(3\). **Step 2: Rewrite the Logarithmic Equation in Exponential Form** Recall that the logarithmic equation \(\log_{b} a = c\) can be rewritten in its exponential form as: \[ b^{c} = a \] Applying this to our equation: \[ 3^{3} = x \] **Step 3: Calculate the Exponential Expression** Now, compute \(3^{3}\): \[ 3^{3} = 3 \times 3 \times 3 = 27 \] **Step 4: Write the Solution** Thus, the solution to the equation is: \[ x = 27 \] **Verification (Optional):** To verify, substitute \(x = 27\) back into the original equation: \[ \log_{3} 27 = 3 \] Since \(3^{3} = 27\), the equation holds true. **Final Answer:** \[ x = 27 \]