Solve Exponent Equation (Fraction Base) (Level 1)

This math topic involves solving exponential equations where the bases are fractions. The main skill practiced here is determining the unknown exponent that equates the fractional base to another fractional value. Each equation is formatted as a fraction raised to the power of x equals another fraction. Participants must find the correct missing exponent from multiple-choice options. The focus is on grasping how different exponents affect the resultant value of a fraction base, refining their understanding of logarithms and exponent rules. This topic is introductory, laying foundational knowledge in the study of logarithms.

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

more

Solve Exponent Equation (Fraction Base)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Solve for the missing exponent

14x=164\frac{1}{4}^{x} = \frac{1}{64}

?

Logarithms - Solve Exponent Equation (Fraction Base) Worksheet

Mobius Math Club logo
Math worksheet on 'Logarithms - Solve Exponent Equation (Fraction Base) (Level 1)'. Part of a broader unit on 'Logarithms - Intro' Learn online: app.mobius.academy/math/units/logarithms_intro/
1
Solve for the missing exponent
A LaTex expression showing 1 over 2 to the power of x = 1 over 16
a
x = 3
b
x = 13
c
x = 4
d
x = -5
e
x = -1
f
x = 9
2
Solve for the missing exponent
A LaTex expression showing 1 over 2 to the power of x = 1 over 4
a
x = -2
b
x = 4
c
x = 0
d
x = 2
e
x = -6
f
x = 9
3
Solve for the missing exponent
A LaTex expression showing 1 over 10 to the power of x = 1 over 100
a
x = 7
b
x = -4
c
x = -8
d
x = 10
e
x = 2
f
x = 1
4
Solve for the missing exponent
A LaTex expression showing 1 over 3 to the power of x = 1 over 81
a
x = 6
b
x = 1
c
x = -4
d
x = 4
e
x = 8
f
x = 5
5
Solve for the missing exponent
A LaTex expression showing 1 over 6 to the power of x = 1 over 216
a
x = 3
b
x = 2
c
x = -1
d
x = -7
e
x = 8
f
x = -2
6
Solve for the missing exponent
A LaTex expression showing 1 over 3 to the power of x = 1 over 27
a
x = 7
b
x = -6
c
x = -3
d
x = -5
e
x = 3
f
x = 12
7
Solve for the missing exponent
A LaTex expression showing 1 over 3 to the power of x = 1 over 9
a
x = 0
b
x = 10
c
x = 7
d
x = 2
e
x = -5
f
x = -1