SOLUTION: solve: 2^(x+1)=e^x

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Question 236518: solve: 2^(x+1)=e^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%28x%2B1%29=e%5Ex Start with the given equation.


ln%282%5E%28x%2B1%29%29=ln%28e%5Ex%29 Take the natural log of both sides.


%28x%2B1%29ln%282%29=x%2Aln%28e%29 Pull down the exponents using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29


%28x%2B1%29ln%282%29=x%2A1 Evaluate the natural log of 'e' to get 1.


%28x%2B1%29ln%282%29=x Multiply


x%2Aln%282%29%2Bln%282%29=x Distribute


ln%282%29=x-x%2Aln%282%29 Subtract x%2Aln%282%29 from both sides.


ln%282%29=x%281-ln%282%29%29 Factor out the GCF 'x'


ln%282%29%2F%281-ln%282%29%29=x Divide both sides by 1-ln%282%29.


So the solution is x=ln%282%29%2F%281-ln%282%29%29