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LogarithmsAlgebraHigh schoolabout 0:40

Evaluate log base 2 of 1/32: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: log_2(1/32) = -5.

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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 2 of 1/32.
2. Step by step
1. $2^{\,y} = \frac{1}{32}$
  Ask: what power of the base gives the number?
2. $\frac{1}{32} = 2^{-5}$
  Write both numbers as powers of the same prime factors
3. The answer
$\log_{2}\left(\frac{1}{32}\right) = -5$
log_2(1/32) = -5
4. Check
- Check: 2^-5 ≈ 0.03125.

Transcript

The problem. Here is the problem: Evaluate log base 2 of 1 over 32. Evaluate the logarithm of 1 over 32 with base 2.

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 1 over 32 equals 2 to the power negative 5.

The answer. So the answer is log 2(1 over 32) equals negative 5. 2 raised to negative 5 gives 1 over 32 exactly.

Check. Check: 2 to the power negative 5 approximately 0.03125.

About logarithms

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

Evaluate log base 2 of 1/32: Logarithms Step-by-Step Lesson