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#1 2006-09-16 11:45:50

Dilbert
Member
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
Member
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
Moderator
Registered: 2005-12-04
Posts: 3,791

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
Member
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.

wave

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.up

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
Moderator
Registered: 2005-12-04
Posts: 3,791

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
Moderator
Registered: 2005-12-04
Posts: 3,791

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
Member
Registered: 2006-05-05
Posts: 1,470

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
Member
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
Member
Registered: 2006-06-01
Posts: 110

Re: stuck

Oops.. Thanks Ricky...up


Letter, number, arts and science
of living kinds, both are the eyes.

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