Question 12
Solve the equation,
log25√x+log416x=6
Solution:
log25√x+log416x=6log25√x+log216xlog24=6log25√x+log216x2=62log25√x+log216x=12log2(5√x)2+log216x=12log2(25x)+log216x=12log2(25x)(16x)=12log2400x2=12400x2=212x2=10.24x=3.2
Question 13
Given that 2 log2 (x – y) = 3 + log2x + log2 y.
Prove that x2 + y2– 10xy = 0.
Solution:
2 log2 (x – y) = 3 + log2x + log2 y
log2 (x– y)2 = log2 8 + log2 x + log2y
log2 (x– y)2 = log2 8xy
(x – y)2 = 8xy
x2– 2xy + y2 = 8xy
x2 + y2 – 10xy = 0 (proven)
Question 14 (2 marks):
Given 2p + 2p = 2k. Express p in terms of k.
Solution:
2p+2p=2k2(2p)=2k2p=2k212p=2k−1p=k−1
Given 2p + 2p = 2k. Express p in terms of k.
Solution:
2p+2p=2k2(2p)=2k2p=2k212p=2k−1p=k−1