Question

if square root of 2401 = square root of 7 raise to the power x then find the value of x

Answer 1

√2401=√7^x
49=7^x/2
7^2=7^x/2
2=x/2
x=4

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Answer 2

The value of x is 4.

Given,

An equation $\sqrt{2401} = \sqrt{7}^{x}$.

To Find,

The value of x.

Solution,

The given equation is

$\sqrt{2401} = \sqrt{7}^{x}$

Now, we will simplify this equation

The value of √2401 is 49

and the value of $\sqrt{7}^{x}$ will be $7^{x/2}$

Now, substituting these values in the equation

$7^{x/2} = 49$

Also, 49 is equal to 7²

So,

$7^{x/2} = 7^{2}$

Since the bases are same, so we can equate the powers

x/2 = 2

x = 4

Hence, the value of x is 4.

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