Short Questions (Question 12 – 14)


Question 12
Solve the equation,  log25x+log416x=6

Solution:
log25x+log416x=6log25x+log216xlog24=6log25x+log216x2=62log25x+log216x=12log2(5x)2+log216x=12log2(25x)+log216x=12log2(25x)(16x)=12log2400x2=12400x2=212x2=10.24x=3.2




Question 13
Given that 2 log2 (xy) = 3 + log2x + log2 y
Prove that x2 + y2– 10xy = 0.

Solution:
2 log2 (xy) = 3 + log2x + log2 y
log2 (xy)2 = log2 8 + log2 x + log2y
log2 (xy)2 = log2 8xy
(xy)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=2k1p=k1