SOLUTION: 4^X-2=3^2X EXPRESS RATIONAL SOLUTION TO THE NEAREST THOUSANDTH

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Question 624380: 4^X-2=3^2X EXPRESS RATIONAL SOLUTION TO THE NEAREST THOUSANDTH
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28x-2%29=3%5E%282x%29

ln%284%5E%28x-2%29%29=ln%283%5E%282x%29%29

%28x-2%29ln%284%29=2x%2Aln%283%29

x%2Aln%284%29-2%2Aln%284%29=2x%2Aln%283%29

-2%2Aln%284%29=2x%2Aln%283%29-x%2Aln%284%29

-2%2Aln%284%29=x%282%2Aln%283%29-ln%284%29%29

%28-2%2Aln%284%29%29%2F%282%2Aln%283%29-ln%284%29%29=x

x+=+%28-2%2Aln%284%29%29%2F%282%2Aln%283%29-ln%284%29%29

x+=+-3.419

So the answer is roughly x+=+-3.419