Math Is Fun Forum

jacks

Member

Registered: 2012-11-21

Posts: 132

exponential and logarithmic equation

number of real solution of

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: exponential and logarithmic equation

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

jacks

Member

Registered: 2012-11-21

Posts: 132

Re: exponential and logarithmic equation

Yes Bobbym you are right. Would you like to explain me, Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: exponential and logarithmic equation

The simplest idea is to use numerics, that means plot it first.

This immediately gives initial estimates for iteration.

You can explore a bit more with graphing to convince yourself that there are only two and this I felt would be adequate for this problem.

But, locating all the roots in non polynomial equations can be tricky. One way to prove that these are the only two would be to show that the curves continue decreasing and therefore never touch the x axis again.

Of course, whether or not this would be sufficient depends on where this problem originates. If it is a school or contest problem then there is almost without a doubt a clever idea that reduces the problem to an easy and clean solution. Therefore, I would continue to look for it.

But, if this problem originates from the real world we might have to be satisfied with the above suggestions.

Wait a second, there is someone in here right now that would take great delight in doing what she thought I could not. I will cease my efforts and let her succeed, only for the sake of chivalry of course.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: exponential and logarithmic equation

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: exponential and logarithmic equation

How do you know what software was used? Or even if software was used.  Wolfram Alpha, Sage and Geogebra are available to everyone for free, why do you call them exotic? You can use any language, even a graphing calculator to do this. But it still does not address the real question - "How many roots are there?"

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: exponential and logarithmic equation

Yes. the number of roots is still a question.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: exponential and logarithmic equation

Iput it in wolfram alpha module. It gave two roots synonymous with what bobbym gave ( I had thought the graph and values were given by bob bundy as usual.) It can be safely assumed that there are only two values. I agree wolfram alpha is easier than what is to be done in excel. That too excel gives only one value at a time depending on the starting value.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}