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Class 9 SELINA Solutions Maths Chapter 8 - Logarithms

Logarithms Exercise Ex. 8(A)

Solution 1

(i)

 

 

(ii)

 

 

(iii)

 

 

(iv)

open parentheses 81 close parentheses to the power of 3 over 4 end exponent equals 27
rightwards double arrow log subscript 81 27 equals 3 over 4 space left square bracket By space definition space of space logarithm comma space straight a to the power of straight b equals straight c rightwards double arrow log subscript straight a straight c equals straight b right square bracket 

Solution 2

(i)

(ii)

(iii)

(iv)

Solution 3

Solution 4

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Solution 5

(i)

(ii)

(iii)

Solution 6

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(ii)

 

(iii)

 

 

(iv)

 

 

(v)

 

(vi)

 

 

Solution 7

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(ii)

 

 

(iii)

 

 

(iv)

 

 

(v)

 

 

(vi)

 

Solution 8

  

Solution 9

  

Solution 10

Solution 11

  

Solution 12

begin mathsize 14px style log space open parentheses straight x squared minus 21 close parentheses equals 2
rightwards double arrow straight x squared minus 21 equals 10 squared
rightwards double arrow straight x squared minus 21 equals 100
rightwards double arrow straight x squared equals 121
rightwards double arrow straight x equals plus-or-minus 11 end style

Logarithms Exercise Ex. 8(B)

Solution 1

(i)

(ii)

(iii)

(iv)

(v)

Solution 2

(i)

(ii)

(iii) 

Solution 3

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(ii)  

 

 

 

 

(iii)  

 

 

Solution 4

 

 

 

Solution 5

 

 

 

 

Solution 6

 

 

Solution 7

(i) 

(ii)

(iii)

(iv)

Solution 8

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(ii)

 

 

 

(iii)

 

 

 

(iv)

 

Solution 9

 

 

 

 

 

Solution 10

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(ii)

 

 

(iii)

 

 

(iv)

 

Solution 11

(i)

 

 

(ii)

 

 

(iii)

 

 

 

(iv)

 

 

(v)

 

 

 

(vi)

 

 

Solution 12

(i)

 

 

(ii)

 

 

 

(iii)

 

 

 

(iv)

log space 15 equals log open parentheses 15 over 10 cross times 10 close parentheses
space space space space space space space space space space space equals log open parentheses 15 over 10 close parentheses plus log space 10 space
space space space space space space space space space space space equals log open parentheses 3 over 2 close parentheses plus 1 space space space space space space space space space space space space space space space space space space space space left square bracket because log space 10 equals 1 right square bracket
space space space space space space space space space space space equals log space 3 minus log space 2 plus 1 space space space space space space space space space space space space space left square bracket because log space straight m minus log space straight n equals log open parentheses straight m over straight n close parentheses right square bracket
space space space space space space space space space space space equals 0.4771 minus 0.3010 plus 1
space space space space space space space space space space space equals 1.1761

 

 

(v)

 

(vi)

 

 

 

Solution 13

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(ii)

 

 

Solution 14

  

Solution 15

  

Solution 16

  

Logarithms Exercise Ex. 8(C)

Solution 1

 

(i)

 

 

(ii)

 

 

(iii)

 

 

Solution 2

 

 

(i)

 

 

(ii)

 

Solution 3

Solution 4

Solution 5

 

(i)

 

 

 

(ii)

 

 

 

(iii)

Consider space the space given space expression :
2 space log subscript 3 straight A equals 5 straight x space minus space 3 straight y
rightwards double arrow 2 space log subscript 3 straight A equals 5 space log subscript 3 straight m minus 3 log subscript 3 straight n
rightwards double arrow log subscript 3 straight A squared equals log subscript 3 straight m to the power of 5 minus log subscript 3 straight n cubed
rightwards double arrow log subscript 3 straight A squared equals log subscript 3 open parentheses straight m to the power of 5 over straight n cubed close parentheses
rightwards double arrow straight A squared equals open parentheses straight m to the power of 5 over straight n cubed close parentheses
rightwards double arrow straight A equals square root of open parentheses straight m to the power of 5 over straight n cubed close parentheses end root

 

Solution 6

(i)

(ii)

Solution 7

Solution 8

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(ii)

 

 

Solution 9

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(ii)

 

 

 

(iii)

 

 

Solution 10

Given space log space straight x space equals space 2 straight m minus straight n comma space log space straight y equals straight n minus 2 straight m space and space log space straight z equals 3 straight m minus 2 straight n
log fraction numerator straight x squared straight y cubed over denominator straight z to the power of 4 end fraction equals logx squared straight y cubed minus logz to the power of 4
equals log space straight x squared plus log space straight y cubed minus log space straight z to the power of 4
equals 2 log space straight x plus 3 log space straight y minus 4 log space straight z
equals 2 left parenthesis 2 straight m minus straight n right parenthesis plus 3 left parenthesis straight n minus 2 straight m right parenthesis minus 4 left parenthesis 3 straight m minus 2 straight n right parenthesis
equals 4 straight m minus 2 straight n plus 3 straight n minus 6 straight m minus 12 straight m plus 8 straight n
equals negative 14 straight m plus 9 straight n

Solution 11

  

Logarithms Exercise Ex. 8(D)

Solution 1

 

 

Solution 2

 

 

 

 

 

 

 

 

Solution 3

 

(i)

 

(ii)

 

Solution 4

 

Solution 5

 

 

Solution 6

 

Solution 7

 

 

Solution 8

Solution 9

(i)

 

 (ii)

Solution 10

 

   

 

Solution 11

 

 

 

Solution 12

 

 

 

Solution 13


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution 14

 

 

 

 

Solution 15

 

 

 

Solution 16

  

Solution 17

  

Solution 18

  

Solution 19

  

Solution 20

  

Solution 21

Solution 22

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