SOLUTION: Solve the equation: (ln(40 × sqrt(3)))/(ln(4x)) =(ln(45)) /(ln(3x) )

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Question 1197361: Solve the equation:
(ln(40 × sqrt(3)))/(ln(4x)) =(ln(45)) /(ln(3x) )
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I haven't yet found an algebraic solution to the equation, although I plan to keep working on it.

But I graphed the two expressions on a graphing calculator and found that they are equal when each of them is equal to 3/2 or 1.5; working back from that I can determine that the solution to the equation is

x+=+root%283%2C75%29

It is my hope that other tutors will look at this and find an algebraic path to the answer -- maybe using the result I found, or maybe not....

Here is how far I got on an algebraic solution.

%28ln%2840%2Asqrt%283%29%29%29%2F%28ln%284x%29%29=%28ln%2845%29%29%2F%28ln%283x%29%29













The value x+=+root%283%2C75%29 satisfies that last equation; but I haven't been able to solve that equation to get that solution.