1975 AHSME Problems/Problem 19
Which positive numbers satisfy the equation ?
By the change-of-base formula, we can simplify the left side of the equation: .
We see that this in fact simplifies to , which will always equal the right side of the equation, since they are the same exact expressions.
But we have to be careful because . Plugging in , the left side would equal , and definitely does not equal .
Besides , can take on any positive value, and the equation would work. Therefore, the answer is ~jiang147369