# ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 9 Logarithms

## ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 9 Logarithms

Exercise 9.1

Question 1.

Convert the following to logarithmic form:

(i) 52 = 25

(ii) a5 =64

(iii) 7x =100

(iv) 9° = 1

(v) 61 = 6

(vi) 3-2 = (frac { 1 }{ 9 })

(vii) 10-2 = 0.01

(viii) (81)(frac { 3 }{ 4 }) = 27

Solution:

Question 2.

Convert the following into exponential form:

(i) log2 32 = 5

(ii) log3 81=4

(iii) log3(frac { 1 }{ 3 })= -1

(iv) log3 4= (frac { 2 }{ 3 })

(v) log8 32= (frac { 5 }{ 3 })

(vi) log10 (0.001) = -3

(Vii) log2 0.25 = -2

(viii) loga ((frac { 1 }{ a })) =-1

Solution:

Question 3.

By converting to exponential form, find the values of:

(i) log2 16

(ii) log5 125

(iii) log4 8

(iv) log9 27

(v) log10(.01)

(vi) log7 (frac { 1 }{ 7 })

(vii) log5 256

(Viii) log2 0.25

Solution:

Question 4.

Solve the following equations for x.

Solution:

Question 5.

Given log10a = b, express 102b-3 in terms of a.

Solution:

Question 6.

Given log10 x= a, log10 y = b and log10 z =c,

(i) write down 102a-3 in terms of x.

(ii) write down 103b-1 in terms of y.

(iii) if log10 P = 2a + (frac { b }{ 2 })– 3c, express P in terms of x, y and z.

Solution:

Question 7.

If log10x = a and log10y = b, find the value of xy.

Solution:

Question 8.

Given log10 a = m and log10 b = n, express (frac { { a }^{ 3 } }{ { b }^{ 2 } }) in terms of m and n.

Solution:

Question 9.

Given log10a= 2a and log10y = –(frac { 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:

Question 10.

If log2 y = x and log3 z = x, find 72x in terms of y and z.

Solution:

Question 11.

If log2 x = a and log5y = a, write 1002a-1 in terms of x and y.

Solution:

Exercise 9.2

Question 1.

Simplify the following :

Solution:

Question 2.

Evaluate the following:

Solution:

Question 3.

Express each of the following as a single logarithm:

Solution:

Question 4.

Prove the following :

(i) log10 4 ÷ log10 2 = l0g3 9

(ii) log10 25 + log10 4 = log5 25

Solution:

Question 5.

If x = 100)a , y = (10000)b and z = (10)c, express

Solution:

Question 6.

If a = log10x, find the following in terms of a :

(i) x

(ii) log10(sqrt [ 5 ]{ { x }^{ 2 } })

(iii) log105x

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

If x = log10 12, y = log4 2 x log10 9 and z = log10 0.4, find the values of

(i)x-y-z

(ii) 7x-y-z

Solution:

Question 10.

If log V + log3 = log π + log4 + 3 log r, find V in terns of other quantities.

Solution:

Question 11.

Given 3 (log 5 – log3) – (log 5-2 log 6) = 2 – log n , find n.

Solution:

Question 12.

Given that log10y + 2 log10x= 2, express y in terms of x.

Solution:

Question 13.

Express log102+1 in the from log10x.

Solution:

Question 14.

Solution:

Question 15.

Given that log m = x + y and log n = x-y, express the value of log m²n in terms of x and y.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solve for x:

Solution:

Question 19.

Given 2 log10x+1= log10250, find

(i) x

(ii) log102x

Solution:

Question 20.

Solution:

Question 21.

Prove the following :

(i) 3log 4 = 4log 3

(ii) 27log 2 = 8log 3

Solution:

Question 22.

Solve the following equations :

(i) log (2x + 3) = log 7

(ii) log (x +1) + log (x – 1) = log 24

(iii) log (10x + 5) – log (x – 4) = 2

(iv) log105 + log10(5x+1) = log10(x + 5) + 1

(v) log (4y – 3) = log (2y + 1) – log3

(vi) log10(x + 2) + log10(x – 2) = log103 + 31og104.

(vii) log(3x + 2) + log(3x – 2) = 5 log 2.

Solution:

Question 23.

Solve for x :

log3 (x + 1) – 1 = 3 + log3 (x – 1)

Solution:

Question 24.

Solution:

Question 25.

Solution:

Question 26.

Solution:

Question 27.

If p = log1020 and q = log1025, find the value of x if 2 log10 (x +1) = 2p – q.

Solution:

Question 28.

Show that:

Solution:

Question 29.

Prove the following identities:

Solution:

Question 30.

Solution:

Question 31.

Solve for x :

Solution:

Multiple Choice Questions

correct Solution from the given four options (1 to 7):

Question 1.

If log√3 27 = x, then the value of x is

(a) 3

(b) 4

(c) 6

(d) 9

Solution:

Question 2.

If log5 (0.04) = x, then the vlaue of x is

(a) 2

(b) 4

(c) -4

(d) -2

Solution:

Question 3.

If log0.5 64 = x, then the value of x is

(a) -4

(b) -6

(c) 4

(d) 6

Solution:

Question 4.

If log10(sqrt [ 3 ]{ 5 }) x = -3, then the value of x is

Solution:

Question 5.

If log (3x + 1) = 2, then the value of x is

Solution:

Question 6.

The value of 2 + log10 (0.01) is

(a)4

(b)3

(c)1

(d)0

Solution:

Question 7.

Solution:

Chapter Test

Question 1.

Solution:

Question 2.

Find the value of log√3 3√3 – log5 (0.04)

Solution:

Question 3.

Prove the following:

Solution:

Question 4.

If log (m + n) = log m + log n, show that n = (frac { m }{ m-1 })

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solve the following equations for x:

Solution:

Question 8.

Solve for x and y:

Solution:

Question 9.

If a = 1 + logxyz, 6 = 1+ logy zx and c=1 + logzxy, then show that ab + bc + ca = abc.

Solution:

You might also like