Question

120. If (25)150 = (25x)50 , then the value of x will be :(a) 53(b) 54(c) 52(d) 5

Answer 1

The value of x will be 3.

Given : (25)150 = (25x)50

To Find : Value of x

Solution :

25 X 150 = 25x X 50

Cancelling 25 on both sides, we get-

150 = x X 50

50x = 150

x = 150/50 = 3

Therefore, the value of x is 3.

Answer 2

Question - If (25)^150 = (25x)^50 , then the value of x will be :(a) 5^3(b) 5^4(c) 5^2(d) 5

The value of x will be (b) 5^4.

Given - Equation

Find - Value of x

Solution - Firstly solving the Left Hand Side of equation.

${25}^{150} = {(5 \times 5)}^{150}$

${25}^{150} = {( {5}^{2} )}^{150}$

${25}^{150} = {5}^{300}$

Now, solving the Right Hand Side of equation

${(25x)}^{50} = { ({5}^{2} )}^{50} \times {x}^{50}$

${(25x)}^{50} = { ({5} )}^{100} \times {x}^{50}$

As both the sides are equal as per the question. So, relating the two sides.

${5}^{300} = {5}^{100} \times {x}^{50}$

${(x)}^{50} = {5}^{300} \div {5}^{100}$

${(x)}^{50} = {5}^{300 - 100}$

${(x)}^{50} = {5}^{200}$

${(x)}^{50} = {5}^{4 \times 50}$

${(x)}^{50} = { ({5}^{4} )}^{50}$

$x = {5}^{4}$

Hence, (b) 5⁴ is the correct value of x.

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