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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
2. Express each of the following in exponential form: (i)
(ii)
(iii)
(iv)
Solution: (i)
(ii)
(iii)
(iv)
3. Solve for x:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iv)
(v)
(vi)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(vii)
(viii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iv)
(v)
(vi)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
7. Evaluate: (i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution: (i)
(ii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iii)
(iv)
(v)
(vi)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iv)
(v)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(i)
(ii)
(iii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
4. Prove that:
Solution:
5. Find x, if:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iii)
(iv)
8. Solve for x: (i)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(ii)
(iii)
(iv)
Solution: (i)
(ii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
10. State, true or false: (i)
(ii)
(iii) If,
, then x=2. (iv)
Solution: (i)
(ii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iii)
(iv)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(iii)
(iv)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(v)
(vi)
13. Given: , find:
(i) x
(ii) log102x
Solution: (i)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
16. If 3(log5-log3)-(log5-2log6)=2-logx, find x.
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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.
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(ii)
(iii)
6. Simplify: (i)
(ii)
Solution: (i)
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
6. If a2+b2=23ab, show that:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
9. Find x, if:
(i)
(ii) Solution:
(i)
(ii)
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
12. Given: 𝐥𝐨𝐠 𝒙
𝐥𝐨𝐠 𝒚=
𝟑
𝟐 and log (xy) = 5; find the values of x and y.
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
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:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
14. Solve:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
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
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
(ii) 13x-y-z
Solution:
(i)
18. Solve for x,
Solution:
19. Evaluate:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
20. Show that:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms
21. If , find x.
Solution:
22. Evaluate:
Solution:
Concise Selina Solutions for Class 9 Maths Chapter 8-
Logarithms