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LogarithmsAlgebraHigh schoolabout 0:39

Evaluate log base e of 10: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: ln(10) ≈ 2.302585093.

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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 e of 10.
2. Step by step
1. $e^{\,y} = 10$
  Ask: what power of the base gives the number?
2. $\ln(10) \approx 2.302585093$
  Evaluate the natural logarithm
3. The answer
$\ln\left(10\right) \approx 2.302585093$
ln(10) ≈ 2.302585093
4. Check
- Check: e^2.302585093 ≈ 10.

Transcript

The problem. Here is the problem: Evaluate log base e of 10. Evaluate the logarithm of 10 with base e.

Step by step. Ask: what power of the base gives the number? Evaluate the natural logarithm. ln(10) has no simpler exact form, so it is evaluated numerically.

The answer. So the answer is ln(10) approximately 2.302585093. e raised to 2.302585093 gives 10 (to 10 significant digits).

Check. Check: e squared.302585093 approximately 10.

About logarithms

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

Evaluate log base e of 10: Logarithms Step-by-Step Lesson