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LogarithmsAlgebraHigh schoolabout 0:36

Evaluate log base 9 of 27: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: log_9(27) = 3/2.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Evaluate log base 9 of 27.
2. Step by step
1. $9^{\,y} = 27$
  Ask: what power of the base gives the number?
2. $27 = 9^{\frac{3}{2}}$
  Write both numbers as powers of the same prime factors
3. The answer
$\log_{9}\left(27\right) = \frac{3}{2}$
log_9(27) = 3/2
4. Check
- Check: 9^1.5 ≈ 27.

Transcript

The problem. Here is the problem: Evaluate log base 9 of 27. Evaluate the logarithm of 27 with base 9.

Step by step. Ask: what power of the base gives the number? Write both numbers as powers of the same prime factors. Comparing prime exponents shows 27 equals 9 to the power 3 over 2).

The answer. So the answer is log 9(27) equals 3 over 2. 9 raised to 3 over 2 gives 27 exactly.

Check. Check: 9 to the power 1.5 approximately 27.

About logarithms

Evaluate logarithms and solve logarithmic equations using the laws of logs.

Evaluate log base 9 of 27: Logarithms Step-by-Step Lesson