Algebra with Logarithms - Binomial over Binomial and Constant

Level 2

This math topic focuses on solving logarithmic equations involving algebraic expressions where a binomial is divided by another binomial and a constant. It involves simplifying these expressions and solving for variables such as \(w\), \(m\), \(p\), and \(x\). Each question provides a logarithmic equation with a specific base, and students are required to find the value of the variable that satisfies the equation. They can choose from multiple-choice answers for each problem. This is an advanced exploratory exercise on logarithm functions.

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

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Algebra with Logarithms - Binomial over Binomial and Constant Worksheet

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Algebra with Logarithms - Binomial over Binomial and Constant
1
Simplify and solve for w
A LaTex expression showing \log sub {2 } {{(\frac{{4w + 8}}{{5w - 8}})}} = 3
a A LaTex expression showing w = 4
b A LaTex expression showing w = 2
c A LaTex expression showing w = 1
d A LaTex expression showing w = 3
2
Simplify and solve for w
A LaTex expression showing \log sub {2 } {{(\frac{{3w + 5}}{{5w - 4}})}} = 3
a A LaTex expression showing w = 0
b A LaTex expression showing w = 1
c A LaTex expression showing w = 3
d A LaTex expression showing w = 2
3
Simplify and solve for m
A LaTex expression showing \log sub {3 } {{(\frac{{2m + 7}}{{3m - 2}})}} = 2
a A LaTex expression showing m = 3
b A LaTex expression showing m = 1
c A LaTex expression showing m = 2
d A LaTex expression showing m = 0
4
Simplify and solve for p
A LaTex expression showing \log sub {2 } {{(\frac{{9p + 6}}{{4p - 5}})}} = 3
a A LaTex expression showing p = 2
b A LaTex expression showing p = 1
c A LaTex expression showing p = 3
d A LaTex expression showing p = 4
5
Simplify and solve for m
A LaTex expression showing \log sub {2 } {{(\frac{{3m - 9}}{{2m - 6}})}} = 5
a A LaTex expression showing m = 3
b A LaTex expression showing m = 5
c A LaTex expression showing m = 4
d A LaTex expression showing m = 2
6
Simplify and solve for x
A LaTex expression showing \log sub {2 } {{(\frac{{6x - 4}}{{2x - 3}})}} = 3
a A LaTex expression showing x = 3
b A LaTex expression showing x = 2
c A LaTex expression showing x = 4
d A LaTex expression showing x = 1
7
Simplify and solve for m
A LaTex expression showing \log sub {2 } {{(\frac{{9m + 7}}{{5m - 3}})}} = 3
a A LaTex expression showing m = 1
b A LaTex expression showing m = 3
c A LaTex expression showing m = 2
d A LaTex expression showing m = 0
8
Simplify and solve for q
A LaTex expression showing \log sub {3 } {{(\frac{{5q - 7}}{{2q - 8}})}} = 2
a A LaTex expression showing q = 6
b A LaTex expression showing q = 7
c A LaTex expression showing q = 4
d A LaTex expression showing q = 5