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Logarithm

Meaning, Equation to Words as Values (Fractions) (Level 1)

This math topic focuses on the fundamental concepts of logarithms involving fractions. It particularly emphasizes understanding the relationship between logarithmic expressions and their equivalences in power (exponential) form. The problems ask students to interpret logarithm equations, such as \(\log_{\frac{1}{6}} \frac{1}{36} = 2\), and determine which of the provided answers correctly represents the equation in exponential form. The answers consist of two options, one correct and one incorrect, where students must identify which transformation from logarithmic to exponential form is accurate. This helps solidify the comprehension of logarithms as inverse operations to exponentiation with fractional bases and results.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Meaning, Equation to Words as Values (Fractions)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

What does the logarithm equation mean?

log⁡18164=2\log _{\frac{1}{8}} \frac{1}{64} = 2

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Logarithms - Meaning, Equation to Words as Values (Fractions) Worksheet

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Math worksheet on 'Logarithms - Meaning, Equation to Words as Values (Fractions) (Level 1)'. Part of a broader unit on 'Logarithms - Intro' Learn online: app.mobius.academy/math/units/logarithms_intro/
1
A LaTex expression showing \log sub 1 over 6 1 over 36 = 2
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }1 over 36 \text{, you would}\\\text{raise }1 over 6 \text{ to the power of }2
b A LaTex expression showing \text{To result in }1 over 6 \text{, you would}\\\text{raise }2\text{ to the power of }1 over 36
2
A LaTex expression showing \log sub 1 over 3 1 over 27 = 3
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }3\text{, you would}\\\text{raise }1 over 27 \text{ to the power of }1 over 3
b A LaTex expression showing \text{To result in }1 over 27 \text{, you would}\\\text{raise }1 over 3 \text{ to the power of }3
3
A LaTex expression showing \log sub 1 over 7 1 over 49 = 2
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }2\text{, you would}\\\text{raise }1 over 49 \text{ to the power of }1 over 7
b A LaTex expression showing \text{To result in }1 over 49 \text{, you would}\\\text{raise }1 over 7 \text{ to the power of }2
4
A LaTex expression showing \log sub 1 over 2 1 over 8 = 3
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }1 over 8 \text{, you would}\\\text{raise }1 over 2 \text{ to the power of }3
b A LaTex expression showing \text{To result in }1 over 8 \text{, you would}\\\text{raise }3\text{ to the power of }1 over 2
5
A LaTex expression showing \log sub 1 over 10 1 over 1,000 = 3
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }1 over 1,000 \text{, you would}\\\text{raise }3\text{ to the power of }1 over 10
b A LaTex expression showing \text{To result in }1 over 1,000 \text{, you would}\\\text{raise }1 over 10 \text{ to the power of }3
6
A LaTex expression showing \log sub 1 over 5 1 over 25 = 2
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }1 over 25 \text{, you would}\\\text{raise }1 over 5 \text{ to the power of }2
b A LaTex expression showing \text{To result in }1 over 5 \text{, you would}\\\text{raise }1 over 25 \text{ to the power of }2
7
A LaTex expression showing \log sub 1 over 8 1 over 64 = 2
What does the logarithm equation mean?
a A LaTex expression showing \text{To result in }2\text{, you would}\\\text{raise }1 over 64 \text{ to the power of }1 over 8
b A LaTex expression showing \text{To result in }1 over 64 \text{, you would}\\\text{raise }1 over 8 \text{ to the power of }2