Hmna wrote:For the equation a^x/a^y=a^-10 and (a^y)^3=a^-x, if a>1 what is the value of x
A)2.5
B)-7.5
C)2
D)1
The second equation can be rephrased as a^(3y) = a^(-x).
Dividing the rephrased second equation by the first, we get:
a^(3y) / (a^x/a^y) = a^(-x) / a¯¹�
a^(3y) * (a^y/
a^x) =
a¹�/
a^x
a^(4y) =
a¹�
4y = 10
y = 10/4 = 2.5.
Substituting y = 2.5 into a^(3y) = a^(-x), we get:
a^(3 * 2.5) = a^(-x)
a^(7.5) = a^(-x)
7.5 = -x
x = -7.5.
The correct answer is
B.
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