Solve the given logarithmic equation.
\[
\log _{3} x=4
\]
Answer
Final Answer: The solution to the equation \(\log _{3} x=4\) is \(x = \boxed{81}\).
Step 1 ：The given equation is in logarithmic form. To solve for x, we need to convert it into exponential form. The base of the logarithm becomes the base of the exponent on the other side of the equation. The number on the other side of the equation becomes the exponent, and the result of the exponentiation is the number we're taking the logarithm of.
Step 2 ：Let's identify the base and the exponent. Here, the base is 3 and the exponent is 4.
Step 3 ：Using the properties of logarithms, we can write the equation in exponential form as \(3^4 = x\).
Step 4 ：Solving the equation gives us \(x = 81.0\).
Step 5 ：Final Answer: The solution to the equation \(\log _{3} x=4\) is \(x = \boxed{81}\).
