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Algebra

Exponential Functions

Exponential Equations

         

Given \(9^a = 27^{10} \), where \(a\) is a positive integer, what is the value of \(a\)?

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

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

\(x\) and \(y\) are real numbers that satisfy \(45y = 81^x\) and \(5y = 3^{x + 64}\). What is the value of \(x\)?

Solve for \(x \)

\[ 5 ^ x + 5 ^{x-1} + 5 ^ {x-2} = 3875 . \]

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