Math Is Fun Forum

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Simplify expression Math

1.    [    2x/ (x^2  - 6x + 9)   -    1/(x+1)   - 8/ (x^2 - 2x - 3)  ]

2.  sq.rt x/ x

3.  ln e^7

4.  e ^(ln 3)

5.  3 (n +1) ! / (5n !)

6.     1/(3+x)  -  1/3 
    ---------------------------
                  x

7.   e ^ (1 + ln x)

8.  e^ (3 ln x)

Thank you for helping me.     

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Simplify expression Math

#2.)  sq.rt x/x => sq.rt x/(sq.rtx)^2 => 1/sq.rt(x)
#3.)  ln e^7 => "ln" means to say "e" to what power is e up 7.  So answer is 7.
#4.)  ln3 says "e up what power is 3", and e^(what) is therefore 3.
#5.)  3/5ths of (n+1), because all the numbers below cancel out, 1 x 2 x 3 x 4...
#8.)  x^3 but I can't explain it, just because 2^9 is 512 and 2^3 is 8 and 8^3 is 512.

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igloo myrtilles fourmis

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Simplify expression Math

Isn't Q8: xe³ ?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Simplify expression Math

Maybe, but I still think it's x^3 just from my example.
Take this example:
Replace e with 4 and ln with log base 4 and replace x with 16.
4^(3 times log base 4 of 16) = 4^6 = 4096

(Like 4^(2*3)=64*64 and 4^2=16,  16^3 = 64^2= 4096)

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igloo myrtilles fourmis

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Simplify expression Math

.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Simplify expression Math

bossk, I got the same answer, but I still want to know
what this rule is called that gets you from your 2nd to 3rd phrase.

Or some links that show it again somewhere online.

Last edited by John E. Franklin (2007-08-23 11:34:06)

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igloo myrtilles fourmis

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Simplify expression Math

I just googled exponents rules and this is the first one I got:

http://www.purplemath.com/modules/exponent.htm

about halfway down you can see:

Their explanation is pretty good, but if you don't believe it, check out the wiki: http://en.wikipedia.org/wiki/Exponentiation (scroll down to "Identities and properties")

Last edited by bossk171 (2007-08-23 13:19:15)

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Gorilla

Guest

Re: Simplify expression Math

Thank you BoseK171,  John E Franklin,  and Identity

I am still trying to understand.  I thank you for the answers. 
I will visit the website.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Simplify expression Math

For #8

EITHER

OR

And the answer to #7 is xe.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Simplify expression Math

Read links, thanks bosk.
Totally unreal Jane, meaning beautiful.
Also, now I see with repetitive multiplying that
this power order does not matter, as long as the
base stays the same and you work from the base out to the exponents.
Like, ((e^2)^3)^4 = ((e^4)^3)^2.
Makes sense when you expand into multiplying.
But you have to be weary when the exponents are combined first,
like e^(2^3) or e^2^(3^4)...  Can't switch those around.

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igloo myrtilles fourmis

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Simplify expression Math

I see, I had made the mistake of:

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Re: Simplify expression Math

Thank you JaneFairfax   Even after the replies were posted you took your time to answer me.
Thankx once again.

Thank you Identity & John E. Franklin, for admitting that you were WRONG in certain areas of the Math answers. Thank you for your honesty. Honesty is important. Remember ENRON !