Questions: Solve for (n) in the equation below. It may [ log 3 729=n n= ]

Solve for (n) in the equation below. It may [ log 3 729=n n= ]
Transcript text: Solve for $n$ in the equation below. It may \[ \begin{array}{l} \log _{3} 729=n \\ n=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Rewrite the logarithmic equation in exponential form

The equation \(\log_{3} 729 = n\) can be rewritten in its exponential form: \[ 3^n = 729 \]

Step 2: Express 729 as a power of 3

We know that \(729\) is a power of \(3\). Let's find the exponent: \[ 3^6 = 729 \]

Step 3: Equate the exponents

Since \(3^n = 3^6\), the exponents must be equal: \[ n = 6 \]

Final Answer

\(\boxed{n = 6}\)

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