SSC CHSL 2020 PYQ — Question 70

We need to compare the power of both sides.

(a^a)^b= a^{a x b}

[{(2/3)³}^(2x+3)]^(-3/4) = [{(2/3)^2/3}^3x+7]^(-6/5)

As we can see on both sides base number is name 2/3 so we can easily compare power of both sides.

3(2x+3)(-3/4) = (2/3)(3x+7)(-6/5)

9(2x+3)/4 = 4(3x+7)/5

45(2x+3)= 16(3x+7)

90x + 135 = 48x + 112

90x - 48x = 112 - 135

42x = -23

And we need to find the value of 

√(2 – 42x) = √{2 – (-23)} = √2+23 =  √25 = 5

So, the value of √(2 – 42x) is 5.