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Class 9 SELINA Solutions Maths Chapter 8: Logarithms

Logarithms Exercise Ex. 8(A)

Solution 1(a)

Correct option: (i) 6

Solution 1(b)

Correct option: (ii) 32

Solution 1(c)

Correct option: (iii) 9

Solution 1(d)

Correct option: (iv) 16

Solution 1(e)

Correct option: (i)

Solution 1(f)

Correct option: (ii)

Solution 2

(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 3

(i)



(ii)



(iii)



(iv)

Solution 4

 

Solution 5

(i)


(ii)


(iii)


(iv)

 
(v)

 
(vi)


(vii)


(viii)

Solution 6

(i)

(ii)

(iii)

 

Solution 7

(i)

 

(ii)

 

(iii)


(iv)




(v)



(vi)

Solution 8

(i)



(ii)



(iii)



(iv)



(v)



(vi)

Solution 9

 

Solution 10

 

Logarithms Exercise Ex. 8(B)

Solution 1(a)

Correct option: (i) 1

Solution 1(b)

Correct option: (ii) 2

Solution 1(c)

Correct option: (iii) 6

Solution 1(d)

Correct option: (iv)

Solution 1(e)

Correct option: (i) 0.001

Solution 1(f)

Correct option: (ii) 13

Positive value = +13

Solution 2

(i)

 
(ii)


(iii)



(iv)


(v)

Solution 3

(i)

(ii)

(iii) 

Solution 4

(i)  



(ii) 


(iii)  

Solution 5

Solution 6

Solution 7

Solution 8

(i) 

(ii)

(iii)

(iv)

Solution 9

(i)



(ii)



(iii)



(iv)

Solution 10

Solution 11

(i)

 
(ii)


(iii)

 
(iv)

Solution 12

(i)


(ii)

 
(iii)

 
(iv)


(v)



(vi)

Solution 13

(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 14

(i)


(ii)

Solution 15

 

Logarithms Exercise Ex. 8(C)

Solution 1(a)

Correct option: (i)

Solution 1(b)

Correct option: (ii) 8

Solution 1(c)

Correct option: (iii)  

Solution 1(d)

Correct option: (iv) 0

Solution 1(e)

Correct option: (i)  

Solution 1(f)

Correct option: (ii)  

Solution 2

 

(i)

 

 (ii)

  

(iii)

Solution 3


(i)


(ii)

Solution 4

Solution 5

Solution 6

 

(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 7

(i)

 

 

(ii)

 

Solution 8

 

Solution 9

(i)


(ii)

Solution 10

(i)


(ii)


(iii)

Logarithms Exercise Ex. 8(D)

Solution 1(a)

Correct option: (i)  

Solution 1(b)

Correct option: (ii) 8

Solution 1(c)

Correct option: (iii) 5

Solution 1(d)

Correct option: (iv) 6

Solution 1(e)

Correct option: (i) log 27

Solution 2

Solution 3

Solution 4

 

(i)

 

(ii)

 

Solution 5

 

Solution 6

 

 

Solution 7

 

Solution 8

Solution 9

Solution 10

(i)

(ii)

Solution 11

    

Solution 12

Solution 13

Solution 14

Solution 15

Logarithms Exercise Test Yourself

Solution 1

Solution 2

 

Solution 3

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

Solution 4

 

Solution 5

 

Solution 6

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 7

 

Solution 8

Solution 9

 

Solution 10

 

Solution 11

 

Solution 12

 

Solution 13

 

Solution 14

Solution 15

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