Standard Level
2.05 Power equations and polynomials
Worksheet
1
Solve for the pronumeral for each of the following equations:
a
30^{n} = \sqrt[3]{30}
b
3^{y} = \dfrac{1}{27}
c
4^{y} = 64
d
7^{x} = 1
e
8^{x} = \dfrac{1}{8^{2}}
f
\left(\sqrt{2}\right)^{k} = 0.5
g
\dfrac{1}{36} = 6^{n}
h
\left(\sqrt{6}\right)^{y} = 36
i
5^{x} = \sqrt[3]{5}
j
8^{x} = \sqrt{8}
k
3^{x} = \sqrt[8]{3}
l
4^{x} = 4^{8}
m
x^{5} = 3^{5}
n
9^{x} = 9^{ - 4 }
o
3^{x} = 3^{\frac{2}{9}}
2
Solve for x for each of the following equations:
a
x^{ - 7 } = \dfrac{1}{6^{7}}
b
7 \left(4^{x}\right) = \dfrac{7}{4^{3}}
c
10^{x} = 0.01
d
5^{ 10 x + 33} = 125
e
5^{ - 3 x -1} = 3125
f
\left(2^{2}\right)^{x + 7} = 2^{3}
g
\left(2^{4}\right)^{ 2 x - 10} = 2^{2}
h
27 \left(2^{x}\right) = 6^{x}
i
9^{y} = 27
j
3^{ 5 x - 10} = 1
k
\dfrac{1}{3^{x - 3}} = \sqrt[3]{9}
l
30 \times 2^{x - 6} = 15
m
a^{x + 1} = a^{3} \sqrt{a}
n
25^{x + 1} = 125^{ 3 x - 4}
o
\left(\dfrac{1}{8}\right)^{x - 3} = 16^{ 4 x - 3}
p
3^{x^{2} - 3 x} = 81
q
\left(\dfrac{8}{3}\right)^{x} = \left(\dfrac{8}{3}\right)^{7}
r
9^{x + 3} = 27^{x}
3
Solve for x for each of the following cubic equations:
a
x^{3} - 125 = 0
b
3 x^{3} = 5 x^{2}
c
x^{3} = - 8
d
8 x^{3} - 125 = 0
e
\left(x + 8\right) \left(x + 4\right) \left(1 + x\right) = 0
f
\left( 5 x - 4\right) \left(x + 3\right) \left(x - 2\right) = 0
g
x^{3} - 49 x = 0
h
512 x^{3} - 125 = 0
i
x^{3} - 3 x^{2} - 18 x + 40 = 0
j
x^{3} - 4 x^{2} - 45 x = 0
k
x^{3} + 9 x^{2} + 27 x + 27 = 0
l
- 64 x^{3} + 48 x^{2} - 12 x + 1 = 0
m
x^{3} - 5 x^{2} - 49 x + 245 = 0
n
x^{3} + 13 x^{2} + 47 x + 35 = 0
o
150 x^{3} + 115 x^{2} - 118 x - 56 = 0
p
729 x^{3} + 8 = 0
q
x^{3} - 5 x^{2} - 4 x + 20 = 0
r
x \left(x - 5\right) \left(x + 7\right) = 8 \left(x - 5\right) \left(x + 7\right)
4
Use technology to solve the following equations:
a
147 x^{3} + 427 x^{2} + 160 x - 84 = 0
b
50 x^{3} + 155 x^{2} + 152 x + 48 = 0
c
64 x^{3} + 40 x^{2} + 54 x + 18 = 0
d
48 x^{3} - 212 x^{2} + 84 x + 209 = - 36
e
- 576 x^{3} + 272 x^{2} - 41 x + 78 = 76
f
- 25 x^{3} + 50 x^{2} - 19 x - 27 = - 45
g
2x^4+5x^3-14x^2-5x+12=0
h
6x^4+9x^3-186x^2+315=0
i
6x^5-5x^4-43x^3+70x^2-24x=0
j
5x^5+x^4-25x^3-5x^2+20x+4=0
5
Solve for the roots of the cubic P \left( x \right) = x^{3} - 2 x^{2} - 5 x + 6 that has a factor of x - 3.
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