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May 25, 2013

# Homework Help: Math

Posted by Michael on Saturday, January 29, 2011 at 7:34pm.

Solve for x:

8^(6x-3)=(1/16)^(5x-9)

• Math - MathMate, Saturday, January 29, 2011 at 8:44pm

We note that the base of the powers are related to 2, for example, 8=2³, and (1/16)=2-4.

8^(6x-3)=(1/16)^(5x-9)
(2³)^(6x-3) = (2-4)^(5x-9)

Apply the laws of exponentiation,
2^(3(6x-3))=2^(-4(5x-9))

Take log to the base 2 on both sides:
3*(6*x-3)=-4*(5*x-9)

Solve for x to get 45/38.

• Math - Henry, Saturday, January 29, 2011 at 9:13pm

8^(6x - 3) = (1/16)^(5x - 9),
(2^3)^(6x - 3) = (1/2^4)^(5x - 9),
(2^3)^(6x - 3) = (2^-4)^(5x - 9),
2^(18x - 9) = 2^(-20x + 36),
18x - 9 = -20x + 36,
18x + 20x = 36 + 9,
38x = 45,
x = 45 / 38 = 1.184.

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