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LogarithmsAlgebraHigh schoolabout 0:43

Evaluate log_8(2): animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: 1/3 ≈ 0.33333333.

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 (0.3 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    log⁡8(2)\log_{8}\left(2\right)
  2. 2. Step by step
    1. log⁡8(2)\log_{8}\left(2\right)
      Read the expression
    2. log⁡8(2)=13\log_{8}\left(2\right) = \frac{1}{3}
      Simplify exactly
    3. log⁡8(2)=13≈0.33333333\log_{8}\left(2\right) = \frac{1}{3} \approx 0.33333333
      Evaluate using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction)
  3. 3. The answer
    13≈0.33333333\frac{1}{3} \approx 0.33333333

    log(2, 8) = 1/3 ≈ 0.33333333

  4. 4. Check
    • Decimal value: 0.333333333333

Transcript

The problem. Here is the problem: log(2, 8). Evaluate a numerical expression.

Step by step. Read the expression. Simplify exactly. Evaluate using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction).

The answer. So the answer is 1 over 3 approximately 0.33333333. Operations are applied in the standard order: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.

Check. Decimal value: 0.333333333333.

About logarithms

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

Evaluate log_8(2): Animated Logarithms Lesson, Step by Step