Logarithms

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

This math topic focuses on the change of base formula for logarithms, specifically converting a logarithm expressed in one base to an equivalent expression in a different base using variables. Problems require the students to transform logarithms like \( \log_y x \) into the form \( \frac{\log_z x}{\log_z y} \) using various specified new bases. Each question provides a specific logarithmic expression and asks students to convert it to a new base, presenting multiple choices for the correct transformed expression. This is designed to enhance understanding of logarithmic functions and their properties.

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

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

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

$A LaTex expression showing \log sub z q$

Convert the given logarithm to the equivalent in base r

a $A LaTex expression showing \frac{\log sub r q}{\log sub r z}$

b $A LaTex expression showing \frac{\log sub q r}{\log sub z r}$

$A LaTex expression showing \log sub y r$

Convert the given logarithm to the equivalent in base n

a $A LaTex expression showing \frac{\log sub r n}{\log sub y n}$

b $A LaTex expression showing \frac{\log sub n r}{\log sub n y}$

$A LaTex expression showing \log sub z m$

Convert the given logarithm to the equivalent in base y

a $A LaTex expression showing \frac{\log sub y m}{\log sub y z}$

b $A LaTex expression showing \frac{\log sub m y}{\log sub z y}$

$A LaTex expression showing \log sub p z$

Convert the given logarithm to the equivalent in base m

a $A LaTex expression showing \frac{\log sub z m}{\log sub p m}$

b $A LaTex expression showing \frac{\log sub m z}{\log sub m p}$

$A LaTex expression showing \log sub p t$

Convert the given logarithm to the equivalent in base w

a $A LaTex expression showing \frac{\log sub t w}{\log sub p w}$

b $A LaTex expression showing \frac{\log sub w t}{\log sub w p}$

$A LaTex expression showing \log sub m q$

Convert the given logarithm to the equivalent in base x

a $A LaTex expression showing \frac{\log sub q x}{\log sub m x}$

b $A LaTex expression showing \frac{\log sub x q}{\log sub x m}$

$A LaTex expression showing \log sub y x$

Convert the given logarithm to the equivalent in base m

a $A LaTex expression showing \frac{\log sub m x}{\log sub m y}$

b $A LaTex expression showing \frac{\log sub x m}{\log sub y m}$

$A LaTex expression showing \log sub w p$

Convert the given logarithm to the equivalent in base n

a $A LaTex expression showing \frac{\log sub n p}{\log sub n w}$

b $A LaTex expression showing \frac{\log sub p n}{\log sub w n}$