How do you solve #2^ { x ^ { 2} - 34x - 2} = 32^ { 5- 8x }#?

1 Answer
Noah G
Nov 28, 2017

#x = -9 or x = 3#

Explanation:

Rewrite in a common base.

#2^(x^2 - 34x - 2) = (2^5)^(5 - 8x)#

#2^(x^2 - 34x - 2) = 2^(25 - 40x)#

We can now eliminate exponents.

#x^2 - 34x - 2 = 25 - 40x#

#x^2 + 6x - 27 = 0#

#(x + 9)(x - 3) = 0#

#x = -9 or 3#

Hopefully this helps!

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