Logarithms

Change of Base - Fraction to Single (Integers) (Level 1)

This topic focuses on practicing the change of base formula for logarithmic expressions. Students are required to convert logarithmic fractions to a simplified form using different bases, all involving integer values. Specifically, these problems help to develop an understanding of manipulating logarithm fractions where both the numerator and the denominator are logarithms to different integer values of the same base, converting them into a single logarithm of a new base. Each question provides multiple-choice answers, challenging students to select the correct simplified logarithm expression.

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

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Logarithms - Change of Base - Fraction to Single (Integers) Worksheet

Logarithms - Change of Base - Fraction to Single (Integers)

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 10 13}{ \log sub 10 2}$

a $A LaTex expression showing \log sub 2 13$

b $A LaTex expression showing \log sub 2 11$

c $A LaTex expression showing \log sub 2 14$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 9 8}{ \log sub 9 2}$

a $A LaTex expression showing \log sub 4 8$

b $A LaTex expression showing \log sub 2 7$

c $A LaTex expression showing \log sub 2 9$

d $A LaTex expression showing \log sub 2 8$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 4 5}{ \log sub 4 6}$

a $A LaTex expression showing \log sub 4 5$

b $A LaTex expression showing \log sub 6 5$

c $A LaTex expression showing \log sub 6 6$

d $A LaTex expression showing \log sub 8 5$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 7 10}{ \log sub 7 3}$

a $A LaTex expression showing \log sub 3 11$

b $A LaTex expression showing \log sub 10 3$

c $A LaTex expression showing \log sub 3 10$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 7 12}{ \log sub 7 2}$

a $A LaTex expression showing \log sub 2 14$

b $A LaTex expression showing \log sub 12 2$

c $A LaTex expression showing \log sub 2 12$

d $A LaTex expression showing \log sub 2 11$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 7 14}{ \log sub 7 8}$

a $A LaTex expression showing \log sub 8 14$

b $A LaTex expression showing \log sub 14 8$

c $A LaTex expression showing \log sub 9 14$

d $A LaTex expression showing \log sub 8 13$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 7 6}{ \log sub 7 5}$

a $A LaTex expression showing \log sub 5 6$

b $A LaTex expression showing \log sub 6 5$

c $A LaTex expression showing \log sub 5 8$

d $A LaTex expression showing \log sub 5 4$

Convert the given logarithm fraction to its simplified form with a change of base

$A LaTex expression showing \frac{ \log sub 6 10}{ \log sub 6 4}$

a $A LaTex expression showing \log sub 10 4$

b $A LaTex expression showing \log sub 4 8$

c $A LaTex expression showing \log sub 4 10$

d $A LaTex expression showing \log sub 4 11$