5.6.2 Indices and Logarithms, SPM Practice (Long Questions)
Question 3:
Given that p = 3r and q = 3t, express the following in terms of r and/ or t.
(a)
(a) log3pq227,
(b) log9p – log27 q.
Solution:
(a)
Given p = 3r, log3 p = r
q= 3t, log3 q =t
log3pq227
= log3 pq2 – log327
= log3 p + log3 q2 – log3 33
= r + 2 log3 q – 3 log3 3
= r + 2 log3 q – 3(1)
= r + 2t – 3
(b)
log9 p– log27 q
=log3plog39−log3qlog327=rlog332−tlog333=r2log33−t3log33=r2−t3
Question 4:
(a) Simplify:
log2(2x + 1) – 5 log4 x2 + 4 log2 x
(b) Hence, solve the equation:
log2(2x + 1) – 5 log4 x2 + 4 log2 x = 4
Solution:
(a)
log2 (2x + 1) – 5 log4 x2 + 4 log2 x
=log2(2x+1)−5log2x2log24+4log2x=log2(2x+1)−52log2x2+log2x4=log2(2x+1)−log2(x2)(52)+log2x4
=log2(2x+1)−log2x5+log2x4=log2(2x+1)(x4)x5=log22x+1x
(b)
log2 (2x + 1) – 5 log4 x2 + 4 log2 x = 4
log22x+1x=4 2x+1x=24 2x+1x=16 2x+1=16x 14x=1x=114