Help with these logorithms?

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cygnus10

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Dec 18, 2013
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So Im really stuck on this problem and I need some help on the work/ how to get to the answer.
Log base 2 of X - Log base 3 of X = 1
 
just to clarify, this problem was a question on one of my tests I took that I couldnt answer. When I took the test, I got this far: log3(x)/log3(2) - log2(x)/log2(3) , which is what youve said, but I cant figure out where to go from there.
 
im still not able to find an answer. This is my work so far, so if someone could check it to see if it was right that would be great. Im not sure what to do next.

log2(x)-log3(x) = 1
log(x)/log(2) - log(x)/log(3) = 1
[log(3x) - log(2x)]/log6 = 1
log(3x) - log(2x) = (log6)(1)
log(3x) - log(2x) = log60

please help me on what to do next?

Edit: thanks for the work guys
 
thanks a lot man. Whew cant believe I made that mistake. Must be because we're learning about simplifying rational functions now.
anyways mate, thanks a bunch. Now I kinda get this problem and it seems a lot easier than before.
 
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