Page 104 - Mathematics_Form_Two

Exponents and radicals

Example 5�17 Example 5�19
Find the value of n in each of the Solve for x and y if 2 × x 3 = y 144.
following equations: Solution

n
(a) 2 n+1 = 64 (b) 4 = 16 From 2 × x 3 = y 144.
Solution = 64 Writing 144 in exponential form gives,
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n+1
(a) 2
Mathematics for Secondary Schools 2 n+1 = 2 6 It follows that, 2 × 4 2. 2
2
4
3
2 ×
144 =
Express 64 in power form to obtain

2 ×
3 =
3
y
x
Comparing exponents gives,
Comparing exponents of the same base
n + 1 = 6

n = 5
gives x =
4 and y =
Therefore, n = 5.
n
(b) 4 = 16 Therefore, x = 4 and y = 2
Express in power form and compare Example 5�20
exponents to obtain x y x y− 1
n
2
4 = 4 Given 4 = 2 and 3 = 9 , find the
n = 2 value of x and y.
Therefore, n = 2. Solution
Simplify 4 = 2 to get
x
y
Example 5�18 2 = 2. Comparing the exponents gives
y
2x
Find the value of b in each of the following ⇒ 2x = y (i)
equations: 3 = 9 y− 1 = 3 = 3 2 y− 2
x
x
3
(a) b = 27 (b) (b + 1) = 64 9 y− 1 = 3= 2 y− 2
3
x
3
x
3 =
Solution Comparing exponents of the same base,
3
(a) b = 27 gives
2
Express 27 in power form to obtain, x = 2y − (ii)
3
b = 3 Solving equations (i) and (ii)
3
b = 3 simultaneously gives
Therefore, b = 3. x = 2 and y = 4 .
3
(b) (b + 1) = 64 3 3
Write 64 in power form to get
3
3
(b + 1) = 4 Example 5�21
b + 1 = 4 Solve for x in each of the following
b = 4 – 1 equations
b = 3 (a) 5 + x 5 (x− 1) = 30.
Therefore, b = 3. (b) 4 + 2 – 20 = 0
x
x
98
Student's Book Form Two
11/10/2024 20:12:21
MATHEMATIC F2 v5.indd 98
MATHEMATIC F2 v5.indd 98 11/10/2024 20:12:21