Short Questions (Question 15 – 17)


Question 15 (4 marks):
(a) Given P=logaQ, state the conditions of a.(b) Given log3y=2logxy3, express y in terms of x.

Solution:
(a)
a > 0, a ≠ 1

(b)
log3y=2logxy3logxyylogxy3=2logxy3logxyy=2y=(xy)2y=x2y21x2=y2yy=1x2


Question 16 (3 marks):
Given 25h+3125p1=1, express p in terms of h.

Solution:
25h+3125p1=125h+3=125p1(52)h+3=(53)p152h+6=53p32h+6=3p33p=2h+9p=2h+93


Question 17 (3 marks):
Solve the equation:logm324logm2m=2

Solution:
logm324logm2m=2logm324logm2mlogmm12=2logm3242(logm2mlogmm)=2logm3242logm2m=2logm324logm(2m)2=logmm2logm(3244m2)=logmm23244m2=m24m4=324m4=81m=±3(3 is rejected)