Question

x^x√x= (x√x)^ find x

Answer 1

Answer: 9/4

Step-by-step explanation:

x^x √x = [x√x]^x

Take a log on both sides

log [(x)^x√x] = log [(x√x)^x]

```````````````log a^n = n*log a```````````

X√x * log x= x * log [ x√x]

``````````````log a*b = log a + log b`````````

X√x * log x = x * [log x + 1/2 log x]

X√x * log x = x * (3/2) * log x

x * log x cancel on both sides

x = 3/2

squaring on both sides

x =9/4

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $\left(x\sqrt{x}\right)^x = x^{x\sqrt{x}}$

To Find:

• Value of x

Solution:

$\implies \left(x\sqrt{x}\right)^x = x^{x\sqrt{x}} \\\\\implies \left(\sqrt{x^2*x}\right)^x = x^{x\sqrt{x}} \\\\\implies \left(\sqrt{x^3}\right)^x = x^{x\sqrt{x}}} \\\\\implies x^{\frac{3}{2}*x} = x^{x\sqrt{x}}} \\\\\text{As, bases are same, we compare the powers,} \\\\\implies \dfrac{3x}{2} = x\sqrt{x} \\\\\implies \dfrac{9x^2}{4} = x^2*x \:\:\:(On\: squaring\:both\:sides) \\\\\implies 9x^2 = 4x^3 \\\\\implies 9 = 4x \:\:\:\:\:(x^2\:gets \:cut)\\\\\bold{\implies x = \dfrac{9}{4}}$

Hope it helps!!