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SChand CLASS 9 Chapter 7 Logarithms TEST

 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)=log1010log102

= 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)=log101log1070

=0log10(7×10)

=0log107log1010

= 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







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