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What is root of equation 2^(x+2) = 8^(4x-1)?

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lemong | Student, Undergraduate | Honors

Posted September 25, 2013 at 4:45 PM via web

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What is root of equation 2^(x+2) = 8^(4x-1)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 25, 2013 at 5:13 PM (Answer #1)

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You need to write 8 as a power of 2, such that:

`2^(x+2) = (2^3)^(4x - 1)`

The following property of exponents can be applied to the right term, such that:

`(2^3)^(4x - 1) = 2^(3(4x - 1))`

Replacing `2^(3(4x - 1))` for `(2^3)^(4x - 1)` yields:

`2^(x+2) = 2^(3(4x - 1))`

You need to equate the exponents both sides, such that:

`x + 2 = 3(4x - 1) => x + 2 = 12x - 3`

You ned to isolate the terms that contain x to one side, such that:

`12x - x = 2 + 3 => 11x = 5 => x = 5/11`

Hence, evaluating the solution to the given equation, yields `x = 5/11.`

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