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LogarithmsAlgebraHigh schoolabout 0:37

Evaluate log base 5 of 0.2: animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: log_5(1/5) = -1.

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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 5 of 0.2.
2. Step by step
1. $5^{\,y} = \frac{1}{5}$
  Ask: what power of the base gives the number?
2. $\frac{1}{5} = 5^{-1}$
  Write both numbers as powers of the same prime factors
3. The answer
$\log_{5}\left(\frac{1}{5}\right) = -1$
log_5(1/5) = -1
4. Check
- Check: 5^-1 ≈ 0.2.

Transcript

The problem. Here is the problem: Evaluate log base 5 of 0.2. Evaluate the logarithm of 1 over 5 with base 5.

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 5 equals 5 to the power negative 1.

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

Check. Check: 5 to the power negative 1 approximately 0.2.

About logarithms

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

Evaluate log base 5 of 0.2: Logarithms Step-by-Step Lesson