Logarithms Concise Class-9th ICSE Maths Selina Publications

Logarithms Concise Class-9th ICSE Mathematics Selina Publications Solutions Chapter-8. We provide step by step Solutions of Exercise / lesson-8 Logarithms  for ICSE Class-9 Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-8 A, Exe-8 B, Exe-8 C, Exe-8 D and Exe-8 E to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics .

Logarithms Concise Class-9th ICSE Mathematics Selina Publications Solutions Chapter-8 by RK Bansal

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–: Select Topics :–

 

Exe-8 A,

Exe-8 B,

Exe-8 C,

Exe-8 D,

 

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Exercise 8 A , Logarithms Concise Class-9th ICSE Mathematics Selina Publications Solutions

Question 1

Express each of the following in logarithmic form:

(i) 5³ = 125

(ii) 3^-2 = …….

(iii) 10^-3 = 0.001

(iv) ………

Answer

Question 2

Express each of the following in exponential form:

(i) log_g 0.125 = -1

(ii) log₁₀0.01 = -2

(iii) log_aA = x

(iv) log₁₀1 = 0

Answer

Question 3

Solve for x: log₁₀ x = -2.

Answer

Question 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

Answer

Question 5

State, true or false:

(i) If log₁₀ x = a, then 10^x = a.

(ii) If x^y = z, then y = log_zx.

(iii) log₂ 8 = 3 and log₈ = 2 = 1/3

Answer

Question 6

Find x, if:

(i) log₃ x = 0

(ii) log_x 2 = -1

(iii) log₉243 = x

(iv) log₅ (x – 7) = 1

(v) log₄32 = x – 4

(vi) log₇ (2x² – 1) = 2

Answer

Question 7

Evaluate:

(i) log₁₀ 0.01

(ii) log₂ (1 ÷ 8)

(iii) log₅ 1

(iv) log₅ 125

(v) log₁₆ 8

(vi) log_0.5 16

Answer

Question 8

If log_a m = n, express a^{n – 1} in terms in terms of a and m.

Answer

Question 9

Given log

(i)…………

(ii)……………

Answer

Question 10

If log …………….

Answer

 

Question 11

Solve for X ……………..

Answer

Question 12

Answer

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Selina Publications Solutions Logarithms Concise Class-9th ICSE Mathematics Exercise 8 B

Question 1

Express in terms of log 2 and log 3:

(i) log 36

(ii) log 144

 (iii) log 4.5

(iv) ……..

  (v) ………… …..

Answer

Question 2

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

(i) 2 log x – log y = 1

(ii) 2 log x + 3 log y = log a

(iii) a log x – b log y = 2 log 3

Answer

Question 3

Evaluate ……….

(i)………………..

(ii) ………………

(iii)……………

Answer

Question 4

Prove that:

…………………….

Answer

Question 5

Find x, if:

x – log 48 + 3 log 2 = 1/3 log 125 – log 3.

Answer

Question 6

Express log₁₀2 + 1 in the form of log₁₀x.

Answer

Question 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)

= 4 log 2 + 2 log 3

Answer

Question 8

Solve for x:

(i)………….

(ii)……………..

(iii)……………..

(iv)………………

Answer

Question 9

Given log x = m + n and log y = m – n, express the value of log ….. in terms of m and n.

Answer

Question 10

State, true or false:

(i) log 1 log 1000 = 0

(ii) ……………………

(iii) If then x = 2

(iv) log x log y = log x + log y

Answer

Question 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 ….

(iv) log 5.4(v) log 60(iv) log …….

Answer

Question 12

If log 2 = 0.3010 and log 3 = 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

Answer

Question 13

Given 2 log₁₀ x + 1 = log₁₀ 250, find :

(i) x(ii) log₁₀ 2x

Answer

Question 14

Given 3 …………………..term of x .

Answer

Question 15

If x = …………………………….a , b and c .

Answer

Question 16

If 3 ……………………………find x .

Answer

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Exercise 8 C, Logarithms Concise Class-9th ICSE Mathematics Selina Publications Solutions

Question 1

If log₁₀ 8 = 0.90; find the value of:

(i) log₁₀ 4

(ii) log ………

(iii) log 0.125

Answer

Question 2

f log 27 = 1.431, find the value of :

(i) log 9

(ii) log 300

Answer

Question 3

If log₁₀ a = b, find 10^{3b – 2} in terms of a.

Answer

Question 4

If log₅ x = y, find 5^{2y+ 3} in terms of x.

Answer

Question 5

Given: log₃ m = x and log₃ n = y.

(i) Express 3^{2x – 3} in terms of m.

(ii) Write down 3^{1 – 2y + 3x} in terms of m and n.

(iii) If 2 log₃ A = 5x – 3y; find A in terms of m and n.

Answer

Question 6

Simplify:

(i) log (a)³ – log a

(ii) log (a)³ +log a

Answer

Question 7

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

Answer

 

Question 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 b^a. a^b = 10

Answer

Question 9

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

(ii) If 2 log y – log x – 3 = 0, express x in terms of y.

(iii) Prove that: log₁₀ 125 = 3(1 – log₁₀2).

Answer

Question 10

Give log x……………….of log ………..

Answer

Question 11

Give log x……………….find x .

Answer

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Solutions of Logarithms Concise Class-9th ICSE Mathematics Selina Publications for Exercise 8 D

Question 1

If 3/2 log a + 2/3 log b – 1 = 0, find the value of a⁹.b⁴.

Answer

Question 2

If x = 1 + log 2 – log 5, y = 2 log3 and z = log a – log 5; find the value of a if x + y = 2z.

Answer

Question 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}

Answer

Question 4

If a² = log x, b³ = log y and 3a² – 2b³ = 6 log z, express y in terms of x and z.

Answer

Question 5

If log ………………..  (log a + log b), show that: a² + b² = 6ab.

Answer

Question 6

If a² + b² = 23ab, show that:

log …………….. (log a + log b).

Answer

Question 7

If m = log 20 and n = log 25, find the value of x, so that: 2 log (x – 4) = 2 m – n.

Answer

Question 8

Solve for x and y ; if x > 0 and y > 0;log xy = log x/y + 2 log 2 = 2.

Answer

Question 9

Find x, if:

(i) log_x 625 = -4

(ii) log_x (5x – 6) = 2

Answer

Question 10

If p =log ……………………………2p-q .

Answer

Question 11

If log………………. x and y .

Answer

Question 12

Given ……………. x and y .

Answer

Question 13

Given log₁₀x = 2a and log₁₀y = ……

(i) Write 10^a in terms of x.

(ii) Write 10^{2b + 1} in terms of y.

(iii) If …………….., express P in terms of x and y.

Answer

Question 14

Solve:

log₅(x + 1) – 1 = 1 + log₅(x – 1).

Answer

Question 15

Solve for x, if:

…………………

Answer

Question 16

if ……………………….x and y .

Answer

Question 17

Give x …………………………find

(i)……………

(ii)……………

Answer

Question 18

Solve for ……………

Answer

Question 19

Evaluate

(i)……….

(ii)…………..

(iii)…………..

Answer

Question 20

Show that

…………….

Answer

Question 21

If log …………find x .

Answer

Question 22

Evaluate ………………….

Answer

 

— End of Logarithms Concise Class-9th ICSE Solutions :–

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