Logarithms

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

This topic focuses on applying the logarithmic change of base formula, specifically converting fractional logarithmic expressions into a standard logarithmic form using variables. It includes exercises that require simplifying expressions like \(\frac{\log_x y}{\log_x q}\) into forms such as \(\log_q y\) or \(\log_y q\). Each problem presents two possible simplified forms, and students are tasked with determining the correct one. This topic is part of an introductory unit on logarithmic functions.

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 (Variables) Worksheet

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Logarithms - Change of Base - Fraction to Single (Variables)
1
A LaTex expression showing \frac{\log sub x y}{\log sub x q}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub q y
b A LaTex expression showing \log sub y q
2
A LaTex expression showing \frac{\log sub y n}{\log sub y m}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub n m
b A LaTex expression showing \log sub m n
3
A LaTex expression showing \frac{\log sub x w}{\log sub x z}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub w z
b A LaTex expression showing \log sub z w
4
A LaTex expression showing \frac{\log sub y z}{\log sub y p}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub p z
b A LaTex expression showing \log sub z p
5
A LaTex expression showing \frac{\log sub r z}{\log sub r x}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub z x
b A LaTex expression showing \log sub x z
6
A LaTex expression showing \frac{\log sub m x}{\log sub m p}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub p x
b A LaTex expression showing \log sub x p
7
A LaTex expression showing \frac{\log sub y r}{\log sub y z}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub z r
b A LaTex expression showing \log sub r z
8
A LaTex expression showing \frac{\log sub m n}{\log sub m r}
Convert the given logarithm fraction to its simplified form with a change of base
a A LaTex expression showing \log sub n r
b A LaTex expression showing \log sub r n