Algebra

Exponential Functions

Exponential Equations

         

Given 9a=27109^a = 27^{10} , where aa is a positive integer, what is the value of aa?

How many real values of xx satisfy the following equation 9x63x55=09^x - 6 \cdot 3^x - 55 = 0?

What is the sum of the absolute values of all the xx's that satisfy the equation (2+3)x+(23)x=4?(2+\sqrt{3})^x+(2-\sqrt{3})^x=4?

xx and yy are real numbers that satisfy 45y=81x45y = 81^x and 5y=3x+645y = 3^{x + 64}. What is the value of xx?

Solve for xx

5x+5x1+5x2=3875. 5 ^ x + 5 ^{x-1} + 5 ^ {x-2} = 3875 .

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