Solve each of the following equations without using calculator.
Problem 1 :
5x = 625
Solution :
5x = 625
625 is a power of 5 and it can be written as 54.
5x = 54
Since the base is same on both sides, exponents can be equated.
x = 4
Problem 2 :
Solution :
Problem 3 :
Solution :
Problem 4 :
3x - 10 = 27x
Solution :
3x - 10 = 27x
3x - 10 = (33)x
3x - 10 = 33x
x - 10 = 3x
2x = 10
x = 5
Problem 5 :
4x + 2 = 8x
Solution :
4x + 2 = 8x
(22)x + 2 = (23)x
22(x + 2) = 23x
2(x + 2) = 3x
2x + 4 = 3x
4 = x
Problem 6 :
Solution :
x2 + 1 = 2x
x2 - 2x + 1 = 0
Solve by factoring.
x2 - x - x + 1 = 0
x(x - 1) - 1(x - 1) = 0
(x - 1)(x - 1) = 0
(x - 1)2 = 0
Taking square root on both sides,
x - 1 = 0
x = 1
Problem 7 :
Solution :
2(x + 4) = 3x2
3x2 - 2x - 8 = 0
Solve by factoring.
3x2 - 6x + 4x - 8 = 0
3x(x - 2) + 4(x - 2) = 0
(x - 2)(3x + 4) = 0
x - 2 = 0 or 3x + 4 = 0
x - 2 = 0 x = 2 |
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