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Given 9a=27109^a = 27^{10} 9a=2710, where aaa is a positive integer, what is the value of aaa?
How many real values of xxx satisfy the following equation 9x−6⋅3x−55=09^x - 6 \cdot 3^x - 55 = 09x−6⋅3x−55=0?
What is the sum of the absolute values of all the xxx's that satisfy the equation (2+3)x+(2−3)x=4?(2+\sqrt{3})^x+(2-\sqrt{3})^x=4?(2+3)x+(2−3)x=4?
xxx and yyy are real numbers that satisfy 45y=81x45y = 81^x45y=81x and 5y=3x+645y = 3^{x + 64}5y=3x+64. What is the value of xxx?
Solve for xx x
5x+5x−1+5x−2=3875. 5 ^ x + 5 ^{x-1} + 5 ^ {x-2} = 3875 . 5x+5x−1+5x−2=3875.
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