INDICES AND LOGARITHMS log 10 8*5 log 10 8 + log 10 5 0.903 +
0.70 = 1.60
Slide 21
INDICES AND LOGARITHMS log a/b = log a - log b
Slide 22
INDICES AND LOGARITHMS log 10 8/5 log 10 8 - log 10 5 0.903 -
0.70 = 0.203
Slide 23
INDICES AND LOGARITHMS log x n n.log x
Slide 24
NATURAL LOGARITHMS The natural logarithm is the logarithm to
the base e e is Euler's number, the base of natural logarithms, e
approximates to 2.718 also known as Napier's constant
Slide 25
SIMULTANEOUS EQUATIONS ( BY ELIMINATION) 1, 2x - y = 2 2, x + y
= 7 Add 1, and 2, (because there is a +y and a y) 3x = 9 x = 3
substitute for x in 1, 6 y = 2 y = 4
Slide 26
SIMULTANEOUS EQUATIONS ( BY ELIMINATION) 1, 2x + y = 7 2, x + y
= 4 Subtract 2, from 1, (because there are two + ys) x = 3
Substitute for x in 1, y = 1
Slide 27
SIMULTANEOUS EQUATIONS ( BY ELIMINATION) 1, 3x + y = 9 2, 2x
+2y = 10 Multiply 1, by 2 3, 6x + 2y = 18 Subtract 2, from 3, 4x =
8 X = 2 Y = 3
Slide 28
SIMULTANEOUS EQUATIONS ( BY SUBSTITUTION 1, y = 5x -3 2, y = 3x
+ 7 5x 3 = 3x + 7 (rearrange) 5x 3x = 7 + 3 2x = 10 x = 5
(substitute in 1) y = (5x5) 3 = 25 - 3 = 22
Slide 29
SIMULTANEOUS EQUATIONS ( BY SUBSTITUTION) 1,2x + y = 7 2, x + y
= 4 x = 4 y Substitute in 1, 2(4 - y) + y = 7 8 -2y + y = 7 8 y = 7
Y = 1 (substitute in 2,) 1 + x = 4 X = 3
Slide 30
SIMULTANEOUS EQUATIONS ( BY GRAPHICAL INTERCEPTION)
Slide 31
WORDED SIMULTANEOUS EQUATION Bill has more money than Mary. If
Bill gave Mary 20, they would have the same amount. While if Mary
gave Bill 22, Bill would then have twice as much as Mary. How much
does each one actually have?