Find a 3x3 Magic Square
where the operation is MULTIPLICATION rather than addition
and the entries are 9 different numbers.

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My Solution.

The only way I found to solve this puzzle was to use properties of EXPONENTS:

In the original problem, we were to look for an arrangement of numbers 1 through 9 that would add up to the same value in any row, column, or diagonal. One solution was this (the sum being 15):

By using the property of exponents when multiplying like bases shown above, all I have to do is choose some x and enter x raised to the values shown in each position of the array above.

The PRODUCT of each row, column, and diagonal is then:

For example, if I choose 2 for my base, I have the following array:

The PRODUCT of each row, column, and diagonal is this case:

Note:

To meet the requirement that all numbers in the array are different, we must choose an x other than 1.