Exercise 8(A) Page: 103...Concise Selina Solutions for Class 9 Maths Chapter 8- Logarithms Exercise...

Concise Selina Solutions for Class 9 Maths Chapter 8-

Logarithms

Exercise 8(A) Page: 103

1. Express each of the following in logarithmic form: (i)

(ii)

(iii)

(iv)

Solution: (i)

(ii)

(iii)

(iv)

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Logarithms

2. Express each of the following in exponential form: (i)

(ii)

(iii)

(iv)

Solution: (i)

(ii)

(iii)

(iv)

3. Solve for x:

Solution:




Logarithms

4. Find the logarithm of:

i. 100 to the base 10

ii. 0.1 to the base 10

iii. 0.001 to the base 10

iv. 32 to the base 4

v. 0.125 to the base 2

vi. 𝟏

𝟏𝟔 to the base 4

vii. 27 to the base 9

viii. 𝟏

𝟖𝟏 to the base 27

Solution: (i)

(ii)

(iii)




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(iv)

(v)

(vi)




Logarithms

(vii)

(viii)




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5. State, true or false:

(i) If log10x=a, then 10x=a.

(ii) If xy=z, then y=logzx.

(iii) log28=3 and log82=𝟏

𝟑

Solution: (i)

(ii)

(iii)




Logarithms

6. Find x if:

(i) log3x=0

(ii) logx2=-1

(iii) log9243=x

(iv) log5(x-7)=1

(v) log432=x-4

(vi) log7(2x2-1)=2

Solution: (i)

(ii)

(iii)




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(iv)

(v)

(vi)




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7. Evaluate: (i)

(ii)

(iii)

(iv)

(v)

(vi)

Solution: (i)

(ii)




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(iii)

(iv)

(v)

(vi)




Logarithms

8. If logam=n, express an-1 in terms of a and m.

Solution:

9. Given log2x=m and log5y=n.

(i) Express 2m-3 in terms of x.

(ii) Express 53n+2 in terms of y.

Solution:




Logarithms

10. If log2x=a and log5y=a, write 72 in terms of x and y.

Solution:

11. Solve for x: log(x-1)+log(x+1)=log21.

Solution:

12. If log(x2-21)=2, show that x=+11.

Solution:




Logarithms

Exercise 8(B) Page: 106 1. Express in terms of log 2 and log 3. (i)

(ii)

(iii)

(iv)

(v)

Solution: (i)

(ii)

(iii)




Logarithms

(iv)

(v)




Logarithms

2. Express each of the following in a form free from logarithm:

(i) 2logx-logy=1

(ii) 2logx+3logy=loga

(iii) alogx-blogy=2log3

Solution: (i)

(ii)

(iii)

3. Evaluate each of the following without using tables:

(i)

(ii)

(iii)

Solution:




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(i)

(ii)

(iii)




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4. Prove that:

Solution:

5. Find x, if:

Solution:




Logarithms

6. Express log102+1 in the form of log10x.

Solution:

7. Solve for x:

(i) log10(x-10)=1

(ii) log(x2-21)=2

(iii) log(x-2)+log(x+2)=log 5

(iv) log(x+5)+log(x-5)=4log2+2log3

Solution: (i)

(ii)




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(iii)

(iv)

8. Solve for x: (i)




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(ii)

(iii)

(iv)

Solution: (i)

(ii)




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(iii)

(iv)

9. Given log x=m+n and log y=m-n, express the value of log 𝟏𝟎𝒙

𝒚𝟐 in terms of m and

n.

Solution:




Logarithms

10. State, true or false: (i)

(ii)

(iii) If,

, then x=2. (iv)

Solution: (i)

(ii)




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(iii)

(iv)

11. If log102=a and log103=b; express each of the following in terms of ‘a’ and ‘b’:

(i) log 12

(ii) log 2.25

(iii) log 𝟐𝟏

𝟒

(iv) log 5.4

(v) log 60

(vi) log 𝟑𝟏

𝟖

Solution:

(i)

(ii)




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(iii)

(iv)




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(v)

(vi)

12. If log 2= 0.3010 and 0.4771; find the value of:

(i) log 12

(ii) log 1.2

(iii) log 3.6

(iv) log 15

(v) log 25

(vi) 𝟐

𝟑 log 8

Solution:

(i)

(ii)




Logarithms

(iii)

(iv)




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(v)

(vi)

13. Given: , find:

(i) x

(ii) log102x

Solution: (i)




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(ii)

14. Given , express y in terms of x.

Solution:

15. If x=(100)a, y=(10000)b and z=(10)c, find in terms of a ,b and c.

Solution:




Logarithms

16. If 3(log5-log3)-(log5-2log6)=2-logx, find x.

Solution:




Logarithms

Exercise 8(C) Page: 108 1. If log108=0.90; find the value of:

(i) log104

(ii) log√𝟑𝟐

(iii) log 0.125

Solution:

(i)

(ii)

(iii)




Logarithms

2. If log 27=1.431, find the value of:

(i) log 9

(ii) log 300

Solution:

(i)

(iii)

3. If log10a=b, find 103b-2 in terms of a.




Logarithms

Solution:

4. If log5x=y, find 52y+3 in terms of x.

Solution:

5. Given: log3m=x and log3n=y.

(i) Express 32x-3 in terms of m.

(ii) Write down 31-2y+3x in terms of m and n.

(iii) If 2log3A=5x-3y; find A in terms of m and n.

Solution:

(i)




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(ii)

(iii)

6. Simplify: (i)

(ii)

Solution: (i)




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(ii)

7. If log (a+b)=log a + log b, find a in terms of b.

Solution:

8. Prove that:

(i) (log a)2-(log b)2=log(a/b).log(ab)

(ii) If a log b+b log a-1=0, then ba.ab=10

Solution:

(i)

(ii)




Logarithms

9.

(i) If log (a+1)=log (4a-3)-log3; find a.

(ii) If 2logy-logx-3=0, express x in terms of y.

Solution: (i)

(ii)

(iii)




Logarithms

10. Given log x=2m-n, log y=n-2m and log z=3m-2n, find in terms of m and n, the

value of:

Solution:

11. Given logx25-logx5=2-logx(1/125); find x.

Solution:




Logarithms




Logarithms

Exercise 8(D) Page: 110

1. If find the value of a9.b4

Solution:

2. If x=1+log2-log5, y=2log3 and z=loga-log5; find the value of a, if x=y=2z.

Solution:




Logarithms

3. If x=log 0.6; y=log 1.25 and z=log 3-2 log 2, find the values of:

(i) x+y-z

(ii) 5 x+y-z

Solution:

(i)




Logarithms

(ii)

4. If a2=logx, b3=log y and 3a2-2b3=6logz, express y in terms of x and z.

Solution:

5. If log 𝒂−𝒃

𝟐 =

𝟏

𝟐(log a+log b), show that a2+b2=6ab.

Solution:




Logarithms

6. If a2+b2=23ab, show that:

Solution:




Logarithms

7. If m=log20 and n=log 25, find the value of x, so that: 2log(x-4)=2m-n.

Solution:

8. Solve for x and y; if x>0 and y>0:

Solution:




Logarithms

9. Find x, if:

(i)

(ii) Solution:

(i)

(ii)




Logarithms

10. If p=log 20 and q=log 25, find the value of x, if 2 log (x+1) = 2p-q.

Solution:

11. If log2(x+y)= log3(x-y)=𝐥𝐨𝐠 𝟐𝟓

𝐥𝐨𝐠 𝟎.𝟐, find the values of x and y.

Solution:




Logarithms

12. Given: 𝐥𝐨𝐠 𝒙

𝐥𝐨𝐠 𝒚=

𝟑

𝟐 and log (xy) = 5; find the values of x and y.

Solution:




Logarithms

13. Given log10x=2a and log10y=𝒃

𝟐

(i) Write 10a in terms of x

(ii) Write 102b+1 in terms of y

(iii) If log10P=3a-2b, express P in terms of x and y.

Solution:




Logarithms

14. Solve:

Solution:




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15. Solve for x, if:

Solution:

16. If a2=log x, b3=log y and

, find c in terms of x and y.

Solution:

17. Given x=log1012, y=log42x log109 and z= log100.4, find:

(i) x-y-z




Logarithms

(ii) 13x-y-z

Solution:

(i)

18. Solve for x,

Solution:

19. Evaluate:

Solution:




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20. Show that:

Solution:




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21. If , find x.

Solution:

22. Evaluate:

Solution:




Logarithms



Exercise 8(A) Page: 103...Concise Selina Solutions for Class 9 Maths Chapter 8- Logarithms Exercise...

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