The logarithm to base a of a number P, is the index x to which a must be raised to be equal to P. Thus if P = ax, then x is the logarithm to the base aof P. We write this as x = log a P. The relationship logaP = x and ax=P are equivalent to each other. ax=P is called the index […]
Category: Mathematics
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Some exponential equation can be reduced to quadratic form as can be seen below. Example : Solve the following equations. a) 2 2x – 6 (2 x) + 8 = 0 b) 5 2x + 4 X 5 x+1 – 125 = 0 c) 3 2x – 9 = 0 Solution a) 2 2x – 6 (2 x) + 8 = 0 (2 x)2 – 6 (2 x) + 8 […]
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Application of Laws of Indices
Solve the following (i) 32 3/5 (ii) 343 2/3 (iii) 64 2/3(iv) 0.001 (v) 14 0 Solution: i) 32 3/5 = (32 1/5) 3 = (5√32) 3 = 2 3 = 8 ii) 343 2/3 = (343 1/3 )2 = (3√343)2 = (7 3)1/3)2 = 72 = 49 iii) 64 2/3 = (64 1/3)2 = (4 3)1/3)2 = 4 2 iv) (0.001)3 = (1/100)3 = (1/10)3)3 = (10 -3)3 = 10 -9 = 1/10 9 v) 14 0 = 1 EVALUATION 1) Simplify the following a) 216 4/3 b) 25 5 c) (0.00001)2 d) […]
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Basic Concept of Laws of Indices
A number of the form am where a is a real number, a is multiplied by itself m times The number a is called the base and the super script m is called the index (plural indices) or exponent. A m x A n = Am + n ——————–Multiplication law Example: X3 xX2 =( X x Xx X) x (X x X) = […]