 Important for :
1
If logx 8 = 0.6, then what is the value of of x is:
» Explain it
C
log8 = 6/10 = 3/5

8 = x3/5

85/3 = X

X = 25 = 32.

Hence, option C is correct.

2
What is the value of 36log6 4 ?
» Explain it
B
We know that : aloga x  = x.

36log6 4  =  (62)log6 4 =  62 log6 4

=  6log6 (42)  =   6log6 (16)  = 16.

Hence, option B is correct.

3
What is the value of log3 5 . log25 27 ?
» Explain it
C
 We know that loga b = log b . log a

 ∴  log3 5 . log25 27 = log 5 × log 27 = log 5 × log 33 log 3 log 25 log 3 log 52

 = log 5 × 3 log 3 = 3 . log 3 2 log 5 2

Hence, option C is correct.

4
What is the value of log9 27 - log27 9 ?
» Explain it
C
log9 27 = m  ⇔  9m = 27  ⇔  32m = 33 ⇔ 2m = 3 = 3/2.

⇒ m = 3/2

And, log27 9 = n ⇔ (27)n = 9  ⇔  33n = 32 ⇔ 3n = 2

 ⇒  n = 2 3

log9 27 - log27 9 = 3/2 - 2/3 = (9-4)/6

⇒ 5/6.

Hence option C is correct.

5
What is the value of [log10 (5 log10 100)]2?
» Explain it
D
[log10 (5 log10 100)]2 = [log10 (5 log10 102)]2

= [log10 (10 log10 10)]2

= [log10 10)]2                                          (∵    log10 10 = 1)

= 12 = 1.

Hence, option D is correct.