SOLUTION: If t = e^x+2 then x =? thanks Brian

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Question 546857: If t = e^x+2 then x =?

thanks
Brian
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If t = e^x+2 then x =?
:
Do you mean: t+=+e%5E%28x%2B2%29, or t+=+e%5Ex+%2B+2?
:
Here is a method for each of them
:
t+=+e%5E%28x%2B2%29
using the nat log
ln%28e%5E%28x%2B2%29%29+=+ln%28t%29%29
the log equiv of exponents
(x+2)*ln(e) = ln(t)
we know the ln of e = 1 so we have
x + 2 = ln(t)
x = ln(t) - 2
Or
t+=+e%5Ex+%2B+2
Subtract 2 from each side
e%5Ex+=+t+-+2
using the nat log
ln%28e%5Ex%29+=+ln%28t-2%29%29
the log equiv of exponents
x*ln(e) = ln(t-2)
we know the ln of e = 1 so we have
x = ln(t-2)