Asked by Michael
Solve for x:
8^(6x-3)=(1/16)^(5x-9)
8^(6x-3)=(1/16)^(5x-9)
Answers
Answered by
MathMate
We note that the base of the powers are related to 2, for example, 8=2³, and (1/16)=2<sup>-4</sup>.
8^(6x-3)=(1/16)^(5x-9)
(2³)^(6x-3) = (2<sup>-4</sup>)^(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.
8^(6x-3)=(1/16)^(5x-9)
(2³)^(6x-3) = (2<sup>-4</sup>)^(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.
Answered by
Henry
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.
(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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