RD Sharma Class 9 Solutions Chapter 2 Exercise 2.2 (Updated for 2021-22)

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RD Sharma Class 9 Solutions Chapter 2 Exercise 2.2

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Question 1.
Assuming that x, y, z are positive real numbers, simplify each of the following:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Prove that:

Solution:

Question 4.
Show that:


Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Find the values of x in each  of the following:

Solution:

Question 11.
If x = 2^1/3 + 2^2/3, show that x³ – 6x = 6.
Solution:

Question 12.
Determine (8x)^x, if 9^{x+ 2} = 240 + 9^x.
Solution:

Question 13.
If 3^x+1 = 9^x-2, find the value of 2^{1 +x}.
Solution:

Question 14.
If 3^4x = (81)^-1 and 10^1/y = 0.0001, find the value of 2^-x+4y
Solution:

Question 15.
If 5^3x = 125 and 10^y = 0.001 find x and y.
Solution:

Question 16.
Solve the following equations:


Solution:

Question 17.

Solution:

Question 18.
If a and b are different positive primes such that

Solution:

Question 19.
If 2^x x 3^y x 5^z = 2160, find x, y and z. Hence, compute the value of 3^x x 2^-y x 5^-z.
Solution:

Question 20.
If 1176 = 2^a x 3^b x 7^c, find the values of a, b and c. Hence, compute the value of 2^a x 3^b x 7^-c as a fraction.
Solution:

Question 21.
Simplify:

Solution:

Question 22.
Show that:

Solution:

Question 23.

Solution:

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