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What is the value of log_(3)243 ? Answer:

Evaluate.\newlinelog⁡3243 \log _{3} 243 \newlineWrite your answer in simplest form.

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Full solution

Q. Evaluate.\newlinelog⁡3243 \log _{3} 243 \newlineWrite your answer in simplest form.
  1. Recognize Problem: Recognize that we need to find the power to which 33 must be raised to get 243243. We know that 33 raised to some integer power will give us 243243. We can write this as 3x=2433^x = 243.
  2. Find Value of x: Determine the value of xx that makes the equation true.\newlineWe can find this by recognizing that 243243 is a power of 33. Specifically, 35=2433^5 = 243.\newlineSo, x=5x = 5.
  3. Conclude Logarithm Value: Conclude that the value of the logarithm is the exponent xx.\newlineSince 35=2433^5 = 243, extlog3243 ext{log}_3 243 is equal to 55.

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