Question

if 2^x - 2^x-1 = 4 then find the value of x^x​

Answer 1

Here is your answer

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Answer 2

Answer:

• $\displaystyle \color{red} \boxed{ {x}^{x} = 27}$

Step-by-step explanation:

Given,

• $\displaystyle{ {2}^{x} - {2}^{x - 1} } = 4$

To Find,

• $\displaystyle{ {x}^{x} = \: ? }$

Solution,

$\displaystyle:\implies { {2}^{x} - {2}^{x - 1} } = 4 \\ \\ \displaystyle:\implies {2}^{x} - \frac{ {2}^{x} }{2} = 4 \\ \\ \displaystyle:\implies {2}^{x} (1 - \frac{1}{2} ) = 4 \\ \\ \displaystyle:\implies {2}^{x} ( \frac{1}{2}) = 4 \\ \\ \displaystyle:\implies {2}^{x} = 8 \\ \\\displaystyle:\implies {2}^{x} = {2}^{3} \\ \\ \displaystyle:\implies \color{red} \boxed{x = 3}$

Putting This value of x in x^x,

$\displaystyle:\implies {x}^{x} = {x}^{x} \\ \\ \displaystyle:\implies {x}^{x} = {(3)}^{(3)} \\ \\ \displaystyle:\implies \color{red} \boxed{ {x}^{x} = 27}$

Required Answer,

• $\displaystyle \color{red} \boxed{ {x}^{x} = 27}$