ShmoopTube

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Here’s your shmoop du jour, brought to you by complex equations.

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If you think solving one is tough, try dating one.

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For the equation: 2 to the power of 2x plus 4 equals 4 to the power of x plus 2...

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Solve for x. And here are your potential answer...

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Interesting...the x's are all in the exponents of this equation...

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…which means we'll be using our basic exponent rules to solve for x.

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Good thing we’ve got those babies in our bag of tricks.

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Ok, so the first thing that's important to notice is that 4 is the same as 2 squared,

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so we can rewrite the second half of our equation as: 2 to the power of 2 times x plus 2.

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2 times x plus 2 equals 2x plus 4... so our equation becomes:

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2 to the 2x plus 4 equals 2 to the 2x plus 4.

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Golly… they’re twins! Aw!

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Ok… what this actually means is that we can substitute

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any real number for x and the equation would be true....

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So D… All real numbers…is our answer.

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Look how adorable they look in matching fisherman hats!

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