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#1 2006-09-16 11:45:50
- Dilbert
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- Registered: 2006-09-05
- Posts: 12
stuck
how do you go about solving e^x=5?
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#2 2006-09-16 12:44:55
- Prakash Panneer
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- Registered: 2006-06-01
- Posts: 110
Re: stuck
Hi,
This is the answer for your question.
Given that,
e^x = 5
Take log on both sides,
log (e^x) = log 5
We know that, log (e^x) = e^log x = x.
Therefore, x = log 5.
x = 0.6990. ( log 5 = 0.6990)
Letter, number, arts and science
of living kinds, both are the eyes.
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#3 2006-09-16 13:04:22
- Ricky
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Re: stuck
Note that the base of log here is the natural number. That is, in common form, log is ln.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#4 2006-09-20 14:12:42
- Prakash Panneer
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- Registered: 2006-06-01
- Posts: 110
Re: stuck
Hi Ricky,
What you said is log x = ln x.
But this incorrect.
The relationship between ln x and log x is:
ln x = 2.303 log x.
I too also made a mistake.
Let me give a correct answer.
Given that,
e^x = 5
Take ln on both sides,
ln (e^x) = log 5
We know that, ln (e^x) = e^ln x = x.
Therefore, x = ln 5.
x = 1.6094 ( ln 5 = 1.6094)
This is our required answer.
Now let us verify the condition
ln x = 2.303 log x ( approximately)
We know, log 5 = 0.6990
ln 5 = 1.6094
ln 5 = 2.303 * 0.6990
= 1.6097
Therefore log and ln are not same.
Last edited by Prakash Panneer (2006-09-20 14:15:06)
Letter, number, arts and science
of living kinds, both are the eyes.
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#5 2006-09-20 15:52:58
- Ricky
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Re: stuck
Actually no. You mistakenly assume that log x means "Log base 10 of x". It is actually unspecified.
If you are an engineer, log x means "Log base 10 of x"
If you are a computer scientist, log x means "Log base 2 of x"
If you are a mathimatican, log x means "Log base e of x"
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#6 2006-09-20 15:54:46
- Ricky
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Re: stuck
And if you are a woodcutter, log x means "Log with an x carved in it"
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#7 2006-09-20 17:31:40
- luca-deltodesco
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- Registered: 2006-05-05
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Re: stuck
...which is why you use ln for log base e, and for any other base, you should use log, with the base in subscript after it like
The Beginning Of All Things To End.
The End Of All Things To Come.
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#8 2006-09-20 20:19:15
- Dross
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- Registered: 2006-08-24
- Posts: 325
Re: stuck
There's also a less well-used convention of
.Bad speling makes me [sic]
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#9 2006-09-21 07:21:16
- Prakash Panneer
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- Registered: 2006-06-01
- Posts: 110
Re: stuck
Oops.. Thanks Ricky...
Letter, number, arts and science
of living kinds, both are the eyes.
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