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RBSE Solutions for Class 11 Maths Chapter 9 लघुगणक Ex 9.1

May 29, 2019 by Prasanna Leave a Comment

Rajasthan Board RBSE Class 11 Maths Chapter 9 लघुगणक Ex 9.1

निम्नलिखित को लघुगणकीय रूप में लिखिए ( प्रश्न संख्या 1 से 6)

प्रश्न 1.
26 = 64
हल-
26 = 64 का लघुगणकीय रूप है log2 64 = 6

प्रश्न 2.
104 = 10000
हल-
104 = 10000 का लघुगणकीय रूप है log10 10000 = 4

प्रश्न 3.
210 = 1024
हल-
210 = 1024 का लघुगणकीय रूप है log2 1024 = 10

प्रश्न 4.
5-2 = \(\frac { 1 }{ 25 }\)
हल-
5-2 = \(\frac { 1 }{ 25 }\) का लघुगणकीय रूप है log5 \(\left( \frac { 1 }{ 25 } \right) \) = – 2

प्रश्न 5.
10-3 = 0.001
हल-
10-3 = 0.001 का लघुगणकीय रूप है log10 0.001 = – 3

प्रश्न 6.
43/2 = 8
हल-
43/2 = 8 का लघुगणकीय रूप है log4 8 = \(\frac { 3 }{ 2 }\)

निम्नलिखित को घातांकीय रूप में लिखिए ( प्रश्न संख्या 7 से 12 )

प्रश्न 7.
log5 25 = 2
हल-
log5 25 = 2 का घातांकीय रूप है 52 = 25

प्रश्न 8.
log3 729 = 6
हल-
log3 729 = 6 का घातांकीय रूप है 36 = 729

प्रश्न 9.
log10 0.001 = -3
हल-
log10 0.001 = -3 का घातांकीय रूप है 10-3 = 0.001

प्रश्न 10.
log10 0.1 = -1
हल-
log10 0.1 = -1 का घातांकीय रूप है 10-1 = 0.1

प्रश्न 11.
log3 \(\left( \frac { 1 }{ 27 } \right) \) = -3
हल-
log3 \(\left( \frac { 1 }{ 25 } \right) \) = -3 का घातांकीय रूप है 3-3 = \(\frac { 1 }{ 27 }\)

प्रश्न 12.
log√2 4 = 4
हल-
log√2 4 = 4 का घातांकीय रूप है (√2)4 = 4

प्रश्न 13.
यदि
log81 x = \(\frac { 3 }{ 2 }\) हो, तो x का मान ज्ञात कीजिए।
हल-
log81 x = \(\frac { 3 }{ 2 }\)
घातांकीय रूप में लिखने पर
x = (81)3/2 = (92)3/2 = 93
x = 9 x 9 x 9
= 729

प्रश्न 14.
यदि log125 \(P=\frac { 1 }{ 6 }\) हो, तो P का मान ज्ञात कीजिए।
हल-
log125 \(P=\frac { 1 }{ 6 }\)
घातांकीय रूप में लिखने पर
x = (125)1/6 = (53)1/6 = (5)3/6
x = (5)1/2 = √5

प्रश्न 15.
यदि log4 m = 1.5 हो, तो m का मान ज्ञात कीजिए।
हल-
log4 m = 1.5
घातांकीय रूप में लिखने पर
(4)1/5 = x
(4)3/2 = x
∴ x = 4 x 2 = 8

प्रश्न 16.
सिद्ध कीजिए
log4[log2{log2(log3 81)}] = 0
हल-
माना log3 81 = x
∴ 3x = 81 = 34
∴ x = 4
अब हमें log2 4 को मान ज्ञात करना है।
माना log2 4 = y
⇒ 2y = 4 = 22
∴ y = 2
∴ log2 4 = 2
L.H.S. में मान रखने पर
∴ log4[log2{log2(log3 81)}] ∵ log3 81 = 4
⇒ log4[log2(log24)] ∵ log2 4 = 2
⇒ log4 [log2 2] ∵ log2 2 = 1
⇒ log4 1 ∵ loga 1 = 0
= 0 = R.H.S. इतिसिद्धम्

RBSE Solutions for Class 11 Maths

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