Algebra
Exponential Functions
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 \(x \)
\[ 5 ^ x + 5 ^{x-1} + 5 ^ {x-2} = 3875 . \]