Math Is Fun Forum

angelus2402004

Member

Registered: 2008-03-20

Posts: 9

Solving Logarithms

I need help with figuring out how to solve these two problems.

1: logbase7(1-x)-logbase7(x+2)=logbase7x^2
2: logbase3(2-x)-logbase3(x+3)=logbase3x

Thank you.

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Solving Logarithms

use the fact:

Last edited by Kurre (2008-04-19 02:22:08)

angelus2402004

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Registered: 2008-03-20

Posts: 9

Re: Solving Logarithms

use the fact:

I can get to that part but I don't know what to do after that.

Daniel123

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Registered: 2007-05-23

Posts: 663

Re: Solving Logarithms

From here it should be straightforward to solve.

angelus2402004

Member

Registered: 2008-03-20

Posts: 9

Re: Solving Logarithms

I get x^3+2x^2+x-1 right? And then what?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Solving Logarithms

Solve.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Solving Logarithms

1.)
Woops, this is wrong, the decimal point was off by one, sorry.
x = 0.19199398 approximately says BASIC program.

Last edited by John E. Franklin (2008-04-19 06:46:53)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Solving Logarithms

my TI-89 says x=1.75487766625 as the answer for the polynomial.

angelus2402004

Member

Registered: 2008-03-20

Posts: 9

Re: Solving Logarithms

My book says the answer is 0.466

John E. Franklin

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Registered: 2005-08-29

Posts: 3,588

Re: Solving Logarithms

@Luis and Daniel, there is a -/+ mixup in Daniels post.

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Solving Logarithms

1.)   0.46557123 is more accurate, BASIC program.

2.)  0.4494897

Last edited by John E. Franklin (2008-04-19 07:01:29)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Solving Logarithms

Oh thanks for pointing that out. I just took Daniel's answer for granted. So:

angelus2402004

Member

Registered: 2008-03-20

Posts: 9

Re: Solving Logarithms

I'm not sure how I would do that on my calculator b/c it's a hp 9g graphing calculator. Is there another way to simplify it more to get the answer?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Solving Logarithms

Does your calculator have a "solve" function as the TI-89 does?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Solving Logarithms

1.)  0.4655712318767681 according to a cubic solving applet on web.

http://tunesmithy.netfirms.com/japplets/iterative_solution_of_cubic.htm

Last edited by John E. Franklin (2008-04-19 07:05:05)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Solving Logarithms

Franklin, is there any method to solve this polynomials of 3 degrees and higher?

Daniel123

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Registered: 2007-05-23

Posts: 663

Re: Solving Logarithms

@Luis and Daniel, there is a -/+ mixup in Daniels post.

Woops. Sorry everyone.

I'm not sure how I would do that on my calculator b/c it's a hp 9g graphing calculator. Is there another way to simplify it more to get the answer?

You could use a manual numerical method if your calculator can't do it itself.

Rearrange to give:

This gives us the iterative formula:

You can see that substituting -1 into the orginal equation gives a negative answer, and substituting 1 gives a positive answer. You therefore know that a root must lie in that interval, as the function is continuous (so it must cross the x-axis in order to go from positive to negative). Pick a value in between, such as 0, and substitute it into the formula (i.e use

). Then keep substituting the value it gives out back into your calculator.

The quickest way to do this is press '0 =' on your calculator. Then type 

and keep pressing equals until the answer converges to as many decimal places as you need.

This is just one of many numerical methods you could use, but it is probably the easiest.

Last edited by Daniel123 (2008-04-19 08:18:54)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Solving Logarithms

Wow, Daniels is smart.  You can do square roots like that, but
I forget how.  I was reading on solving a cubic equation a month ago, but it was so hard I left it on the back burner for now.

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Solving Logarithms

Yeah, I tried to read one of those a while ago. All I remember is that you need to make some kind of substitution that transforms a general cubic equation into one of the form ax³ + bx + c (ie. no quadratic term).

It's easier to solve that than a general cubic, and then you can reverse the substitution to get the original answer. Unfortunately, the method for solving that slightly more specific cubic is still horrendous compared to solving quadratics.

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muhammad777

Member

Registered: 2008-03-23

Posts: 1

Re: Solving Logarithms

hi
I have question about logarithm i am little confused the difference between when used logarithm and when i used natural log
plz give me practical example

your's muhammad

alecia

Guest

Re: Solving Logarithms

Does your calculator have a "solve" function as the TI-89 does?

log x=-3/2

log 3=x
 

log 1/4=x