solve this for me please: |ln x| = 1?
回答 (6)
2009-06-23 2:03 pm
✔ 最佳答案
|ln(x)| = 1ln(x) = ±1
ln(x) = 1
x = e
ln(x) = -1
x = 1/e
x = {1/e, e}
2009-06-23 9:03 pm
if | ln x | = 1, then either ln x = 1 or ln x = -1
if ln x = 1, then e^1 = x ==> x = e
if ln x = -1, then e^-1 = x => x = 1/e
two solutions: x = e or x = 1/e
careful Kahsel... logs can be negative (the range is (-inf , inf)); what you're thinking of is that you can't take the log of a negative number (or 0, for that matter)-- the domain of logs is positive numbers only; however, the range is all real numbers
if ln x = 1, then e^1 = x ==> x = e
if ln x = -1, then e^-1 = x => x = 1/e
two solutions: x = e or x = 1/e
careful Kahsel... logs can be negative (the range is (-inf , inf)); what you're thinking of is that you can't take the log of a negative number (or 0, for that matter)-- the domain of logs is positive numbers only; however, the range is all real numbers
2009-06-23 9:03 pm
x = e
2009-06-23 9:03 pm
Those bars mean 'the magnitude of', which basically means how much do you have, regardless of the sign.
But it doesn't really matter, since logs can never be negative.
Ln x is just shorthand for Log base e of x, or Log e (x) - and a log is equal to 1 when the base and the result are the same.
So basically, when x = e (or about 2.718), |ln x| = 1!
Edit: - yeah, disregard my negative bit thing. Made a mistake - x can't be negative, sorry. Not the answer. So could be e^-1, or 1/e, not just e. ...Yep.
Peh.
But it doesn't really matter, since logs can never be negative.
Ln x is just shorthand for Log base e of x, or Log e (x) - and a log is equal to 1 when the base and the result are the same.
So basically, when x = e (or about 2.718), |ln x| = 1!
Edit: - yeah, disregard my negative bit thing. Made a mistake - x can't be negative, sorry. Not the answer. So could be e^-1, or 1/e, not just e. ...Yep.
Peh.
2009-06-25 10:05 am
lnx=1
x=e^1=e=2.7183
lnx=-1
x=e^-1=0.36788
x=e^1=e=2.7183
lnx=-1
x=e^-1=0.36788
2009-06-24 5:04 pm
|ln(x)| = 1
ln(x) = ±1
x = e^1, e^-1
x = e, 1/e
ln(x) = ±1
x = e^1, e^-1
x = e, 1/e
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