F.4 MATHS

3a) expand (a+b)(a-b)
= a^2 - ab + ab - b^2 = a^2 - b^2

3b) evaluate ( √21 - √5 ) ( √21 + √5 )
By(a), we have ( √21 - √5 ) ( √21 + √5 ) = (√21)^2 - (√5)^2 = 21 - 5 = 16

3c) evaluate log底2 ( √21 - √5 ) +log 底2 ( √21 + √ 5 )
= log底2 [( √21 - √5 ) ( √21 + √5 )] = log底2 [16] = log底2 [2^4] = 4

4a)2 ^(x+1) = 5^(x-1)
2*2^x = 5^x / 5
10 = 5^x/2^x = 2.5^x
Thus, a = 2.5

4b) 2.5^x = 10
log (2.5^x) = log 10
x log2.5 = 1
x = 1/log2.5 = 2.51