Logarithms

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

This math topic focuses on the practice of converting logarithms from one base to another using the change of base formula. Each problem presents a logarithm with an integer base, and students are tasked with rewriting it to an equivalent expression in a different base, typically a fractional one. The questions integrate skills involving understanding and manipulation of logarithmic expressions, reinforcing the concept of logarithms and their properties in logarithmic operations.

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

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

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

Convert the given logarithm to the equivalent in base 3

$A LaTex expression showing \log sub 9 12$

a $A LaTex expression showing \frac{ \log sub 9 12}{ \log sub 9 3}$

b $A LaTex expression showing \frac{ \log sub 3 12}{ \log sub 3 9}$

c $A LaTex expression showing \frac{ \log sub 12 9}{ \log sub 12 3}$

d $A LaTex expression showing \frac{ \log sub 3 9}{ \log sub 3 12}$

Convert the given logarithm to the equivalent in base 5

$A LaTex expression showing \log sub 7 6$

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

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

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

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

Convert the given logarithm to the equivalent in base 8

$A LaTex expression showing \log sub 5 9$

a $A LaTex expression showing \frac{ \log sub 9 5}{ \log sub 9 8}$

b $A LaTex expression showing \frac{ \log sub 5 9}{ \log sub 5 8}$

c $A LaTex expression showing \frac{ \log sub 8 9}{ \log sub 8 5}$

Convert the given logarithm to the equivalent in base 7

$A LaTex expression showing \log sub 10 12$

a $A LaTex expression showing \frac{ \log sub 10 12}{ \log sub 10 7}$

b $A LaTex expression showing \frac{ \log sub 12 10}{ \log sub 12 7}$

c $A LaTex expression showing \frac{ \log sub 7 12}{ \log sub 7 10}$

d $A LaTex expression showing \frac{ \log sub 12 7}{ \log sub 12 10}$

Convert the given logarithm to the equivalent in base 5

$A LaTex expression showing \log sub 2 13$

a $A LaTex expression showing \frac{ \log sub 2 13}{ \log sub 2 5}$

b $A LaTex expression showing \frac{ \log sub 5 2}{ \log sub 5 13}$

c $A LaTex expression showing \frac{ \log sub 5 13}{ \log sub 5 2}$

d $A LaTex expression showing \frac{ \log sub 13 2}{ \log sub 13 5}$

Convert the given logarithm to the equivalent in base 7

$A LaTex expression showing \log sub 10 8$

a $A LaTex expression showing \frac{ \log sub 8 10}{ \log sub 8 7}$

b $A LaTex expression showing \frac{ \log sub 7 10}{ \log sub 7 8}$

c $A LaTex expression showing \frac{ \log sub 7 8}{ \log sub 7 10}$

d $A LaTex expression showing \frac{ \log sub 8 7}{ \log sub 8 10}$

Convert the given logarithm to the equivalent in base 9

$A LaTex expression showing \log sub 7 10$

a $A LaTex expression showing \frac{ \log sub 10 9}{ \log sub 10 7}$

b $A LaTex expression showing \frac{ \log sub 9 10}{ \log sub 9 7}$

c $A LaTex expression showing \frac{ \log sub 9 7}{ \log sub 9 10}$

d $A LaTex expression showing \frac{ \log sub 10 7}{ \log sub 10 9}$

Convert the given logarithm to the equivalent in base 2

$A LaTex expression showing \log sub 5 10$

a $A LaTex expression showing \frac{ \log sub 2 5}{ \log sub 2 10}$

b $A LaTex expression showing \frac{ \log sub 2 10}{ \log sub 2 5}$

c $A LaTex expression showing \frac{ \log sub 10 5}{ \log sub 10 2}$

d $A LaTex expression showing \frac{ \log sub 10 2}{ \log sub 10 5}$