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LogarithmsAlgebraHigh schoolabout 0:33

Evaluate log base 3 of 81: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: log_3(81) = 4.

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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 3 of 81.
2. Step by step
1. $3^{\,y} = 81$
  Ask: what power of the base gives the number?
2. $81 = 3^{4}$
  Write both numbers as powers of the same prime factors
3. The answer
$\log_{3}\left(81\right) = 4$
log_3(81) = 4
4. Check
- Check: 3^4 ≈ 81.

Transcript

The problem. Here is the problem: Evaluate log base 3 of 81. Evaluate the logarithm of 81 with base 3.

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 81 equals 3 to the power 4.

The answer. So the answer is log 3(81) equals 4. 3 raised to 4 gives 81 exactly.

Check. Check: 3 to the power 4 approximately 81.

About logarithms

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

Evaluate log base 3 of 81: Logarithms Step-by-Step Lesson