Algebra with Logarithms - Binomial and Constant

Level 2

This topic focuses on solving logarithmic equations where variables are found within binomial expressions affected by a logarithmic function. It includes advanced problems from a broader unit on logarithm functions, moving individuals through various scenarios to simplify and solve for different variables (designated as w, r, p, q, t, and z) given in the form of \(\log_b (ax + c) = d\). Each question offers multiple choice answers, reinforcing understanding and mastery of logarithmic operations, properties, and their application in algebraic contexts.

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

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Algebra with Logarithms - Binomial and Constant Worksheet

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Algebra with Logarithms - Binomial and Constant
1
Simplify and solve for w
A LaTex expression showing \log sub {2 } {{(4w - 8)}} = 5
a A LaTex expression showing w = 12
b A LaTex expression showing w = 10
c A LaTex expression showing w = 9
d A LaTex expression showing w = 11
2
Simplify and solve for r
A LaTex expression showing \log sub {2 } {{(5r - 8)}} = 5
a A LaTex expression showing r = 10
b A LaTex expression showing r = 7
c A LaTex expression showing r = 8
d A LaTex expression showing r = 9
3
Simplify and solve for p
A LaTex expression showing \log sub {2 } {{(2p - 8)}} = 5
a A LaTex expression showing p = 22
b A LaTex expression showing p = 19
c A LaTex expression showing p = 20
d A LaTex expression showing p = 21
4
Simplify and solve for q
A LaTex expression showing \log sub {6 } {{(2q + 8)}} = 2
a A LaTex expression showing q = 15
b A LaTex expression showing q = 13
c A LaTex expression showing q = 14
d A LaTex expression showing q = 16
5
Simplify and solve for w
A LaTex expression showing \log sub {2 } {{(2w - 4)}} = 5
a A LaTex expression showing w = 19
b A LaTex expression showing w = 18
c A LaTex expression showing w = 20
d A LaTex expression showing w = 17
6
Simplify and solve for t
A LaTex expression showing \log sub {2 } {{(2t + 6)}} = 5
a A LaTex expression showing t = 15
b A LaTex expression showing t = 13
c A LaTex expression showing t = 12
d A LaTex expression showing t = 14
7
Simplify and solve for z
A LaTex expression showing \log sub {9 } {{(2z - 7)}} = 2
a A LaTex expression showing z = 46
b A LaTex expression showing z = 44
c A LaTex expression showing z = 45
d A LaTex expression showing z = 43
8
Simplify and solve for x
A LaTex expression showing \log sub {4 } {{(4x - 8)}} = 2
a A LaTex expression showing x = 7
b A LaTex expression showing x = 8
c A LaTex expression showing x = 5
d A LaTex expression showing x = 6