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Mathematics 21 Online
OpenStudy (jiteshmeghwal9):

Plz help:)

OpenStudy (jiteshmeghwal9):

If \[2x-2x-1=4\] then \[x^x\] is equal to

OpenStudy (jiteshmeghwal9):

@ParthKohli plz help:)

OpenStudy (jiteshmeghwal9):

Oh! i m sorry. It's 2x-2^x-1

OpenStudy (jiteshmeghwal9):

@Sriram x-1 is the power of 2

OpenStudy (anonymous):

Can you write the question once again in more correct form??

OpenStudy (jiteshmeghwal9):

& the answer is 27.

OpenStudy (anonymous):

\[2x-2^{x}-1=4\] Is that the original equation?

OpenStudy (jiteshmeghwal9):

no, the original equation is\[2^x-2^{x-1}=4\]

OpenStudy (anonymous):

8-4=4

OpenStudy (anonymous):

4 can be rewritten as 2^2. 2^x can be rewritten as x*2^(x-1).

OpenStudy (anonymous):

\[2^x - 2^{x-1} = 4\] From this equation by trail let me check for x = 3 \[2^3 - 2^2 = 4\] \[4 = 4\] So, x = 3 satisfies this equation.. \[x^x = 3^3 = 27\]

OpenStudy (anonymous):

\[2^x-2^{x-1}=4 \\ 2^x-\frac{2^x}{2}=4 \\ \frac{2^x}{2}=4\\ 2^x=8 \\ x=3\]

OpenStudy (anonymous):

then \[x^x=3^3=27\]

OpenStudy (jiteshmeghwal9):

K! I have gt it . Thanx, a lot to everyone:)

OpenStudy (anonymous):

@mukushla I want to know once again how you found the value for x above??

OpenStudy (anonymous):

Can you explain your third step???

OpenStudy (jiteshmeghwal9):

& @Sriram i m sorry.

OpenStudy (anonymous):

Alternate way to do it: \[2^{x}-2^{x-1} = 4\] \[2*2^{x-1}-1*2^{x-1} = 2^{2}\] \[2^{x-1}(2-1) = 2^{2}\] \[2^{x-1}(1) = 2^{2}\] \[2^{x-1} = 2^{2}\] X-1=2 X=3

OpenStudy (anonymous):

@waterineyes \[2^x-\frac{2^x}{2}=2^x(1-1/2)=\frac{2^x}{2} \\ \because 2^{x-1}=\frac{2^x}{2^1}\]

OpenStudy (anonymous):

Yes, I got it thanks buddy...

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