Logarithms - Convert Exponent to Logarithm - Fraction Base (Level 1) - Mobius Math

Convert Exponent to Logarithm - Fraction Base (Level 1)

This math topic focuses on converting exponential expressions with fractional bases into logarithmic form. It is an introductory level exercise aimed at helping students understand the relationship between exponentiation and logarithms, specifically when dealing with fractional bases. Each problem presents an exponential equation, \((1/n)^m = 1/p\), and asks students to find the correct logarithmic equivalent. Multiple choice answers are provided for each question, allowing students to select the correct logarithmic form that represents the given exponential equation. This topic is part of a broader unit introducing logarithms.

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

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Convert Exponent to Logarithm - Fraction Base

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

Convert the given exponent to the equivalent in logarithm form

\frac{1}{3}^{2} = \frac{1}{9}

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Logarithms - Convert Exponent to Logarithm - Fraction Base Worksheet

Math worksheet on 'Logarithms - Convert Exponent to Logarithm - Fraction Base (Level 1)'. Part of a broader unit on 'Logarithms - Intro' Learn online: app.mobius.academy/math/units/logarithms_intro/

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 6 to the power of 3 = 1 over 216

a $A LaTex expression showing \log sub 3 1 over 6 = 1 over 216$

b $A LaTex expression showing \log sub 1 over 6 1 over 216 = 3$

c $A LaTex expression showing \log sub 1 over 216 3 = 1 over 6$

d $A LaTex expression showing \log sub 1 over 216 1 over 6 = 3$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 7 to the power of 2 = 1 over 49

a $A LaTex expression showing \log sub 2 1 over 49 = 1 over 7$

b $A LaTex expression showing \log sub 1 over 49 2 = 1 over 7$

c $A LaTex expression showing \log sub 1 over 49 1 over 7 = 2$

d $A LaTex expression showing \log sub 1 over 7 1 over 49 = 2$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 2 to the power of 3 = 1 over 8

a $A LaTex expression showing \log sub 1 over 8 3 = 1 over 2$

b $A LaTex expression showing \log sub 3 1 over 8 = 1 over 2$

c $A LaTex expression showing \log sub 1 over 2 1 over 8 = 3$

d $A LaTex expression showing \log sub 3 1 over 2 = 1 over 8$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 10 to the power of 4 = 1 over 10,000

a $A LaTex expression showing \log sub 1 over 10,000 1 over 10 = 4$

b $A LaTex expression showing \log sub 1 over 10 1 over 10,000 = 4$

c $A LaTex expression showing \log sub 4 1 over 10,000 = 1 over 10$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 2 to the power of 2 = 1 over 4

a $A LaTex expression showing \log sub 1 over 2 1 over 4 = 2$

b $A LaTex expression showing \log sub 1 over 4 2 = 1 over 2$

c $A LaTex expression showing \log sub 1 over 4 1 over 2 = 2$

d $A LaTex expression showing \log sub 2 1 over 4 = 1 over 2$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 5 to the power of 3 = 1 over 125

a $A LaTex expression showing \log sub 3 1 over 125 = 1 over 5$

b $A LaTex expression showing \log sub 3 1 over 5 = 1 over 125$

c $A LaTex expression showing \log sub 1 over 125 3 = 1 over 5$

d $A LaTex expression showing \log sub 1 over 5 1 over 125 = 3$

Convert the given exponent to the equivalent in logarithm form

A LaTex expression showing 1 over 6 to the power of 2 = 1 over 36

a $A LaTex expression showing \log sub 1 over 36 1 over 6 = 2$

b $A LaTex expression showing \log sub 1 over 36 2 = 1 over 6$

c $A LaTex expression showing \log sub 1 over 6 1 over 36 = 2$

d $A LaTex expression showing \log sub 2 1 over 36 = 1 over 6$