1. Functions
Worksheet
1
Solve for x:
a
3^{x} = 27
b
5^{x} = 625
c
7^{x} = 343
d
2^{3x} = 64
e
10^{x-4} = 1000
f
10^{x} = 0.01
g
8^{5x -1} = 64
h
9^{x} = 27
i
3^{ 5 x - 10} = 1
j
b^{2x} = a^{18}
k
a^{x + 1} = a^{3} \sqrt{a}
l
\left(2^{2}\right)^{x + 7} = 2^{3}
2
Solve for x:
a
30 \times 2^{x - 6} = 15
b
\left(\dfrac{1}{9}\right)^{x + 5} = 81
c
2^{x} \times 2^{x + 3} = 32
d
\left(\sqrt{2}\right)^{x} = 0.5
e
27 \left(2^{x}\right) = 6^{x}
f
25^{x + 1} = 125^{ 3 x - 4}
g
\dfrac{1}{3^{x - 3}} = \sqrt[3]{9}
h
5^{ - 3 x -1} = 3125
i
8^{x + 5} = \dfrac{1}{32 \sqrt{2}}
j
7^{x - 2} = \dfrac{1}{49}
3
Find the integer interval in which the solution of the following equations will lie:
a
3^{x} = 57
b
3^{x} = 29
c
2^{x} = \dfrac{1}{13}
d
2^{x} = - 5
4
Consider the equation 3^{x} \times 3^{ n x} = 81.
a
Simplify 3^{x} \times 3^{ n x}.
b
Hence, solve the equation.
5
Solve 3^{x^{2} - 3 x} = 81.
6
Solve \dfrac{25^{y}}{5^{4 - y}} = \sqrt{125}.
7
Solve the following equations:
a
4^{ 2 x} - 65 \times 4^{x} + 64 = 0
b
2^{ 2 x} - 12 \times 2^{x} + 32 = 0
8
The graphs y = 2^{ 5 x} and y = 4^{x - 3} intersect at a certain point.
Find the x-coordinate of the point of intersection.
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