Power Law - Algebra (Base of Constant is Power, Solve X) (Level 1)

This math topic focuses on solving exponential equations using the power law, particularly when a constant base is raised to a variable power (x). The problems explore equalities such as 3^x = 9^2, 2^x = 4^26, and similar expressions. Each question provides six potential values of x as multiple-choice answers. The overall aim is to consolidate an understanding of exponents, including negative and fractional exponents, through solving for the variable x in various exponential settings. This theme is embedded in a broader study unit on exponents.

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

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Exponents - Power Law - Algebra (Base of Constant is Power, Solve X) Worksheet

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Math worksheet on 'Exponents - Power Law - Algebra (Base of Constant is Power, Solve X) (Level 1)'. Part of a broader unit on 'Exponents - Negative, Fractional, and Power Law' Learn online: app.mobius.academy/math/units/exponents_negatives_fractions_and_power_law/
1
Solve for x
A LaTex expression showing 3 to the power of x = 9 to the power of 2
a A LaTex expression showing x=3
b A LaTex expression showing x=6
c A LaTex expression showing x=2
d A LaTex expression showing x=11
e A LaTex expression showing x=4
f A LaTex expression showing x=8
2
Solve for x
A LaTex expression showing 2 to the power of x = 4 to the power of 26
a A LaTex expression showing x=52
b A LaTex expression showing x=87
c A LaTex expression showing x=72
d A LaTex expression showing x=32
e A LaTex expression showing x=97
f A LaTex expression showing x=27
3
Solve for x
A LaTex expression showing 5 to the power of x = 25 to the power of 6
a A LaTex expression showing x=17
b A LaTex expression showing x=21
c A LaTex expression showing x=3
d A LaTex expression showing x=18
e A LaTex expression showing x=19
f A LaTex expression showing x=12
4
Solve for x
A LaTex expression showing 2 to the power of x = 16 to the power of 29
a A LaTex expression showing x=116
b A LaTex expression showing x=6
c A LaTex expression showing x=215
d A LaTex expression showing x=193
e A LaTex expression showing x=17
f A LaTex expression showing x=138
5
Solve for x
A LaTex expression showing 5 to the power of x = 25 to the power of 15
a A LaTex expression showing x=9
b A LaTex expression showing x=27
c A LaTex expression showing x=30
d A LaTex expression showing x=36
e A LaTex expression showing x=51
f A LaTex expression showing x=24
6
Solve for x
A LaTex expression showing 3 to the power of x = 27 to the power of 23
a A LaTex expression showing x=105
b A LaTex expression showing x=21
c A LaTex expression showing x=111
d A LaTex expression showing x=123
e A LaTex expression showing x=69
f A LaTex expression showing x=63
7
Solve for x
A LaTex expression showing 5 to the power of x = 25 to the power of 11
a A LaTex expression showing x=2
b A LaTex expression showing x=24
c A LaTex expression showing x=4
d A LaTex expression showing x=32
e A LaTex expression showing x=22
f A LaTex expression showing x=14