Question 975628
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Actually it's 8<sup>3</sup> not 3<sup>8</sup>.

The base of the log is the base of the exponent. 

log<sub>8</sub>(xy) = 3

becomes the equation

xy = 8<sup>3</sup>

xy = 512           <-- so you had 512, so you must have had 8<sup>3</sup>, not 3<sup>8</sup>.

There are many solutions to that.  There are infinitely many.  Maybe
you were to find just the positive integer solutions. If so,
the solution (x,y) could be any of these:

(1,512) (2,256) (4,128) (8,64) (16,32) (32,16) (64,8) (128,4) (256,2) (512,1)

Edwin</pre>