TEST
Question 1
The value of log216 is
(a) 18
(b) 4
(c) 8
(d) 16
Sol :
(b) 4
log216=log224=4log22 = 4×1 (∵ log2a=1)
= 4
Question 2
If ax=by then
(a) logab=xy
(b) logalogb=xy
(c) logalogb=yx
(d) None of these
Sol :
ax=by
Taking log both sides,
logax=bby
⇒ xloga=ylogb
⇒ logalogb=yx
Question 3
If log 3 = 0.477 and (1000)x=3, then x equals
(a) 0.0159
(b) 0.0477
(c) 0.159
(d) 10
Sol :
log 3 = 0.477
(1000)x=3
Taking log of both sides
xlog 1000 = log3
⇒ x × 3 = log3 (∵ log 1000 = 3)
⇒ 3x = 0.477
⇒ x=0.4773
x = 0.159
Question 4
If log102=0.3010, the value of log105 is
(a) 0.3241
(b) 0.6911
(c) 0.6990
(d) 0.7525
Sol :
log102=0.3010
log105=log10(102)=log1010–log102
= 1 – 0.3010 = 0.6990 (c)
Question 5
If log102=0.3010, the value of log1080 is
(a) 1.6020
(b) 1.9030
(c) 3.9030
(d) None of these
Sol :
(b) 1.9030
log102=0.3010
log1080=log1010×23
=log1010+log1023
=log1010+3log102
= 1 + 3×0.3010
= 1 + 0.9030 = 1.9030
Question 6
If log107=a, then log10(170) is equal to
(a) – (1 + a)
(b) (1+a)−1
(c) a10
(d) 110a
Sol :
(a) – (1 + a)
log107=a
log10(170)=log101–log1070
=0–log10(7×10)
=0–log107–log1010
= 0 – 0 – 1 = – (1 + a)
Question 7
If log 27 = 1.431, then the value of log 9 is
(a) 0.934
(b) 0.945
(c) 0.954
(d) 0.958
Sol :
(c) 0.954
log 27 = 1.431
⇒ log 3³ = 1.431
⇒ 31og 3 = 1.431
⇒ log 3 =1.4313 = 0.477
log 9 = log 3² = 2 log 2
= 2×0.477 = 0.954
Question 8
If log105+log10(5x+1)=log10(x+5)+1, then x is equal to
(a) 1
(b) 3
(c) 5
(d) 10
Sol :
(b) 3
log105+log10(5x+1)=log10(x+5)+1
log105(5x+1)=log10(x+5)+log1010
log10(5x+1)=log1010(x+5)
Comparing, we get
⇒ 5(5x + 1) = 10(x + 5)
⇒ 25x + 5 = 10x + 50
⇒ 25x – 10x = 50 – 5
⇒ 15x = 45
⇒ x=4515=3
⇒ x = 3
Question 9
If logx4=0.4, then the value of x is
(a) 1
(b) 4
(c) 16
(d) 32
Sol :
logx4=0.4
⇒ 4=x0.4
⇒ x=410.4=(22)10.4
= 22×10.4=210.2
= 215=21×51=25
= 2×2×2×2×2 = 32
∴ x = 32
Question 10
The solution of logπ[log2(log7x)]=0 is
(a) 2
(b) π²
(c) 72
(d) None of these
Sol :
logπ[log2(log7x)]=0
⇒ log2(log7x)=π°=1
⇒ log7x=21=2
⇒ x=72
∴ x=72
No comments:
Post a Comment