Questions: Solve the logarithmic equation log3(81)=x x=4 x=7 x=3 x=27

Transcript text: Solve the logarithmic equation $\log _{3}(81)=x$ $x=4$ $x=7$ $x=3$ $x=27$

Solution

Solution Steps

To solve the logarithmic equation $\log_{3}(81) = x$, we need to determine the value of $x$ such that $3^x = 81$. Recognize that 81 is a power of 3, specifically $3^4$. Therefore, $x$ should be 4.

Step 1: Understand the Logarithmic Equation

The given equation is $\log_{3}(81) = x$. This means we need to find the value of $x$ such that $3^x = 81$.

Step 2: Express 81 as a Power of 3

Recognize that 81 can be expressed as a power of 3. Specifically, $81 = 3^4$.

Step 3: Equate the Exponents

Since $3^x = 3^4$, it follows that $x = 4$.

Final Answer

The solution to the equation $\log_{3}(81) = x$ is $\boxed{x = 4}$.

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