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LogarithmsAlgebraHigh schoolabout 0:39

Evaluate log base 10 of 0.001: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: ln(1/1000) = -3.

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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 10 of 0.001.
2. Step by step
1. $10^{\,y} = \frac{1}{1000}$
  Ask: what power of the base gives the number?
2. $\frac{1}{1000} = 10^{-3}$
  Write both numbers as powers of the same prime factors
3. The answer
$\log_{10}\left(\frac{1}{1000}\right) = -3$
ln(1/1000) = -3
4. Check
- Check: 10^-3 ≈ 0.001.

Transcript

The problem. Here is the problem: Evaluate log base 10 of 0.001. Evaluate the logarithm of 1 over 1000 with base 10.

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 1000 equals 10 to the power negative 3.

The answer. So the answer is ln(1 over 1000) equals negative 3. 10 raised to negative 3 gives 1 over 1000 exactly.

Check. Check: 10 to the power negative 3 approximately 0.001.

About logarithms

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

Evaluate log base 10 of 0.001: Animated Step-by-Step Lesson