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

This topic focuses on understanding and interpreting logarithmic equations with fractional bases and results. It requires translating worded expressions of exponential relationships into corresponding logarithmic equations. Each question provides a scenario describing a base raised to a certain power to yield a fractional result, and students must identify the correct logarithmic representation among multiple choices. The problems are framed to enhance the student's grasp of logarithmic fundamentals, particularly handling logarithms involving fractions.

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

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

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Math worksheet on 'Logarithms - Meaning, Words to Equation as Values (Fractions) (Level 1)'. Part of a broader unit on 'Logarithms - Intro' Learn online: app.mobius.academy/math/units/logarithms_intro/
1
Which logarithm equation shows this?
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
a A LaTex expression showing \log sub 3 1 over 1,000 = 1 over 10
b A LaTex expression showing \log sub 1 over 10 1 over 1,000 = 3
c A LaTex expression showing \log sub 3 1 over 10 = 1 over 1,000
d A LaTex expression showing \log sub 1 over 1,000 3 = 1 over 10
e A LaTex expression showing \log sub 1 over 1,000 1 over 10 = 3
2
Which logarithm equation shows this?
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
a A LaTex expression showing \log sub 1 over 6 1 over 36 = 2
b A LaTex expression showing \log sub 1 over 36 2 = 1 over 6
c A LaTex expression showing \log sub 1 over 36 1 over 6 = 2
d A LaTex expression showing \log sub 2 1 over 36 = 1 over 6
3
Which logarithm equation shows this?
A LaTex expression showing \text{To result in }1 over 16 \text{, you would}\\\text{raise }1 over 4 \text{ to the power of }2
a A LaTex expression showing \log sub 1 over 16 1 over 4 = 2
b A LaTex expression showing \log sub 1 over 4 1 over 16 = 2
c A LaTex expression showing \log sub 2 1 over 4 = 1 over 16
d A LaTex expression showing \log sub 1 over 16 2 = 1 over 4
4
Which logarithm equation shows this?
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
a A LaTex expression showing \log sub 1 over 64 2 = 1 over 8
b A LaTex expression showing \log sub 1 over 8 1 over 64 = 2
c A LaTex expression showing \log sub 2 1 over 64 = 1 over 8
d A LaTex expression showing \log sub 1 over 64 1 over 8 = 2
e A LaTex expression showing \log sub 2 1 over 8 = 1 over 64
5
Which logarithm equation shows this?
A LaTex expression showing \text{To result in }1 over 216 \text{, you would}\\\text{raise }1 over 6 \text{ to the power of }3
a A LaTex expression showing \log sub 1 over 6 1 over 216 = 3
b A LaTex expression showing \log sub 1 over 216 3 = 1 over 6
c A LaTex expression showing \log sub 1 over 216 1 over 6 = 3
d A LaTex expression showing \log sub 3 1 over 6 = 1 over 216
6
Which logarithm equation shows this?
A LaTex expression showing \text{To result in }1 over 16 \text{, you would}\\\text{raise }1 over 2 \text{ to the power of }4
a A LaTex expression showing \log sub 4 1 over 16 = 1 over 2
b A LaTex expression showing \log sub 1 over 16 4 = 1 over 2
c A LaTex expression showing \log sub 1 over 2 1 over 16 = 4
d A LaTex expression showing \log sub 4 1 over 2 = 1 over 16
7
Which logarithm equation shows this?
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
a A LaTex expression showing \log sub 1 over 7 1 over 49 = 2
b A LaTex expression showing \log sub 1 over 49 2 = 1 over 7
c A LaTex expression showing \log sub 2 1 over 49 = 1 over 7
d A LaTex expression showing \log sub 2 1 over 7 = 1 over 49
e A LaTex expression showing \log sub 1 over 49 1 over 7 = 2