Question

Given
$\large\sf{5}^{x} - {5}^{x - 2} =3000$
So find the value of $\large\sf \: {(x)}^{x}$
$\:$

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Answer 1

Answer:

3125

Step-by-step explanation:

Given :

$\sf {5}^{x} - {5}^{x - 2} =3000$

To find :

$\mathrm{x^x}$

Solution :

$\longmapsto \mathrm{{5}^{x} - {5}^{x - 2} =3000}$

$\implies \mathrm{{5}^{x} - \dfrac{{5}^x }{5^2} =3000}$

Let 5ˣ = t

$\implies \mathrm{t - \dfrac{t}{25} = 3000}$

$\implies \mathrm{25t - t = 3000 \times 25}$

$\implies \mathrm{24t = 3000 \times 25}$

$\implies \mathrm{t = \dfrac{3000 \times 25}{24}}$

$\implies \mathrm{t = 3125}$

$\implies \mathrm{5^x = 3125}$

Here, as 5⁵, 3125 is t

So, x = 5

So,

$\implies \mathrm{x^{x} = 5^5 = 3125}$

❖ Extra information :

⟡ Law of exponents

$\boxed{\begin{array}{cc}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{array}}$

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Hope it helps!!

Answer 2

Answer:

give some points pl

Step-by-step explanation:

please rishi