SOLUTION: Please solve e^x = 2 using steps

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Question 133333: Please solve e^x = 2 using steps
Found 3 solutions by josmiceli, nycsharkman, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Logs are exponents, and in this problem, x is an exponent,
and so it is also a log. The base of this log is e
I can write x+=+log%28e%2C2%29 This is normally written as
x+=+ln%282%29.I can find this on my calculator.
ln%282%29+=+.693147
x+=+.693147 answer

Answer by nycsharkman(136) About Me  (Show Source):
You can put this solution on YOUR website!
We can get a solution by changing the exponential equation to log form.
Take natural log of both sides of the equation.
In(e^x) = In(2)
The left side becomes x because the natural log of e^x is just x.
We now have this:
x = In(2)
Use calculator to find x.
x = 0.693
NOTE: I also want to add that the decimal number 0.6931471806 can be rounded off to three decimal places. This is why I selected the approximate value for x = 0.693
Is this clear?


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex+=+2 Start with the given equation


ln%28e%5Ex%29+=+ln%282%29 Take the natural log of both sides


x%2Aln%28e%29+=+ln%282%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x%2A%281%29+=+ln%282%29 Evaluate ln%28e%29 to get 1


x+=+ln%282%29 Multiply


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Answer:
So our answer is x+=+ln%282%29 which is approximately x=0.6931471806