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
(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+3125p−1=1, express p in terms of h.
Solution:
25h+3125p−1=125h+3=125p−1(52)h+3=(53)p−152h+6=53p−32h+6=3p−33p=2h+9p=2h+93
Given 25h+3125p−1=1, express p in terms of h.
Solution:
25h+3125p−1=125h+3=125p−1(52)h+3=(53)p−152h+6=53p−32h+6=3p−33p=2h+9p=2h+93
Question 17 (3 marks):
Solve the equation:logm324−log√m2m=2
Solution:
logm324−log√m2m=2logm324−logm2mlogmm12=2logm324−2(logm2mlogmm)=2logm324−2logm2m=2logm324−logm(2m)2=logmm2logm(3244m2)=logmm23244m2=m24m4=324m4=81m=±3(−3 is rejected)
Solve the equation:logm324−log√m2m=2
Solution:
logm324−log√m2m=2logm324−logm2mlogmm12=2logm324−2(logm2mlogmm)=2logm324−2logm2m=2logm324−logm(2m)2=logmm2logm(3244m2)=logmm23244m2=m24m4=324m4=81m=±3(−3 is rejected)