SOLUTION: find the two positive integers that satisfies the equation: {{{log(5,(x))log(4,(x))+log(5,(x))log(3,(x))}}}{{{""=""}}}{{{log(5,(x))log(4,(x))log(3,(x))-log(3,(x))log(4,(x))}}}

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Question 1062933: find the two positive integers that satisfies the equation:

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!



Use the change of base formula to change to logs base 10:  



Get 0 on the right:



Multiply through by LCD = log(3)∙log(4)∙log(5)



Factor out [log(x)]2



Set each factor = 0 and solve:

     

The first factor set = 0 has solution x = 1.

The second factor set equal to 0, we solve for log(x)










So the two solutions are x = 1 and x = 60.

Edwin
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