Question
te the logarithm: \( \log _{3} 729 \). (GRIDDED
Ask by Fuentes Mcguire. in the United States
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \log_{3} 729 = 6 \)
Solution
We need to find x such that 3ˣ = 729.
Step 1: Write down the equation for the logarithm definition.
If log₃ 729 = x, then 3ˣ = 729.
Step 2: Find the power of 3 that equals 729.
3¹ = 3
3² = 9
3³ = 27
3⁴ = 81
3⁵ = 243
3⁶ = 729
Step 3: Conclude the answer.
Since 3⁶ = 729, we have x = 6.
Thus, log₃ 729 = 6.
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Simplify this solution Bonus Knowledge
To solve \( \log_{3} 729 \), we first recognize that 729 is a power of 3. Specifically, \( 729 = 3^6 \). Thus, we can rewrite the logarithm: \[ \log_{3} 729 = \log_{3} (3^6) \] Using the logarithmic property that \( \log_{b} (b^x) = x \), we find: \[ \log_{3} (3^6) = 6 \] Therefore, \( \log_{3} 729 = 6 \). So, the final answer is: **6**
