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.

more
View

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

Mobius Math Academy logo
Exponents - Power Law - Algebra (Base of Constant is Power, Solve X)
1
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=21
b A LaTex expression showing x=19
c A LaTex expression showing x=17
d A LaTex expression showing x=3
e A LaTex expression showing x=18
f A LaTex expression showing x=12
2
Solve for x
A LaTex expression showing 7 to the power of x = 49 to the power of 6
a A LaTex expression showing x=21
b A LaTex expression showing x=12
c A LaTex expression showing x=13
d A LaTex expression showing x=15
e A LaTex expression showing x=19
f A LaTex expression showing x=3
3
Solve for x
A LaTex expression showing 3 to the power of x = 9 to the power of 16
a A LaTex expression showing x=8
b A LaTex expression showing x=2
c A LaTex expression showing x=17
d A LaTex expression showing x=20
e A LaTex expression showing x=32
f A LaTex expression showing x=35
4
Solve for x
A LaTex expression showing 11 to the power of x = 121 to the power of 23
a A LaTex expression showing x=50
b A LaTex expression showing x=58
c A LaTex expression showing x=18
d A LaTex expression showing x=46
e A LaTex expression showing x=42
f A LaTex expression showing x=38
5
Solve for x
A LaTex expression showing 5 to the power of x = 25 to the power of 17
a A LaTex expression showing x=34
b A LaTex expression showing x=49
c A LaTex expression showing x=7
d A LaTex expression showing x=13
e A LaTex expression showing x=10
f A LaTex expression showing x=55
6
Solve for x
A LaTex expression showing 7 to the power of x = 49 to the power of 20
a A LaTex expression showing x=8
b A LaTex expression showing x=32
c A LaTex expression showing x=56
d A LaTex expression showing x=4
e A LaTex expression showing x=76
f A LaTex expression showing x=40
7
Solve for x
A LaTex expression showing 7 to the power of x = 49 to the power of 21
a A LaTex expression showing x=18
b A LaTex expression showing x=10
c A LaTex expression showing x=78
d A LaTex expression showing x=66
e A LaTex expression showing x=42
f A LaTex expression showing x=14
8
Solve for x
A LaTex expression showing 11 to the power of x = 121 to the power of 12
a A LaTex expression showing x=34
b A LaTex expression showing x=4
c A LaTex expression showing x=24
d A LaTex expression showing x=20
e A LaTex expression showing x=32
f A LaTex expression showing x=42