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Algebra Level 1

If 2 x = 4 2^x = 4 , what is 2 x 2x ?


The answer is 4.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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5 solutions

Gian Tuazon
Dec 29, 2016

2 x = 4 2^x=4 ; 2 x = y 2x = y

2 x = 2 2 2^x = 2^2

x = 2 x = 2

2 x = y 2x = y

2 ( 2 ) = y 2(2) = y

4 = y 4 = y

3 Helpful 0 Interesting 0 Brilliant 0 Confused

@Pi Han Goh Lol, why so easy problems? O.o

Nihar Mahajan - 4 years, 5 months ago

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What? This is a hard problem! :(

Pi Han Goh - 4 years, 5 months ago
A W
Jun 1, 2017
  • 2^ x x =4
  • 2^ x x -1=2 (Divide both sides by 2)
  • 2^ x x -2=1 (Divide both sides by 2)
  • 2^0=1
  • x x -2=0
  • x x =2 (Add 2 to both sides)
  • 2 x x =2(2)
  • 2(2)= 4 4
2 Helpful 0 Interesting 0 Brilliant 0 Confused
Munem Shahriar
Jan 25, 2018

2 x = 4 2^x =4

2 x = 2 2 2^x = 2^2

⟹ x = 2 \implies x = 2

Hence 2 x = 2 × 2 = 4 2x = 2 \times 2 = \boxed{4}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nicely done.

Note that you claimed that 2 x = 2 2 2^x = 2^2 which implies that x = 2 x = 2 .

But why can't we claim that e i π = e − i π e^{i \pi} = e^{-i \pi } implies i π = − i π i \pi = - i \pi ?

Pi Han Goh - 3 years, 4 months ago
Anubhav Pal
Dec 30, 2016

2^x=4 x=2 then 2x=2.2=4 Q.E.D

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Lew Sterling Jr
May 28, 2019

2 x = 4 2 x = 2 2 x = 2 2 x = 2 ( 2 ) = 4 \begin{matrix} 2^x=4\\ 2^x=2^2\\ x=2\\\\ 2x\\ =2(2)\\ =\textbf{4} \end{matrix}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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