Math Is Fun Forum

ksa-boy

Guest

solve it please

who can solve for me this :

2 ^ ( x ) * 5 ^ ( y ) = 200

2 ^ ( y ) * 5 ^ ( x ) = 500

whats the value of x and y ?!
i tried more than once but no chance ... help me please this is my first post here

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve it please

By inspection, x = 3, y = 2. (Factorize 200 and 500.)

Well, these particular equations happen to be easily solvable by inspection, but in general, you can take logarithms for such equations. They will then be converted into simultaneous linear equations, which should be easier to solve.

Last edited by JaneFairfax (2007-02-26 07:55:38)

ksa-boy

Guest

Re: solve it please

they way you solved it please please

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve it please

By inspection,
200 = 2[sup]3[/sup]·5[sup]2[/sup]
500 = 2[sup]2[/sup]·5[sup]3[/sup]

But all right, let’s do it systematically …

Taking logarithm on both sides (the log can be to any base; here log[sub]10[/sub] will be fine), you get

Now solve for x and y.

Last edited by JaneFairfax (2007-02-26 10:03:13)

ksa-boy

Guest

Re: solve it please

i got these equations ... but the problem is in solving them ... please solve it

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: solve it please

Last edited by luca-deltodesco (2007-02-26 06:33:03)

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Maelwys

Member

Registered: 2007-02-02

Posts: 161

Re: solve it please

Now ksa-boy, I hope that when you submit your homework you make sure to put luca-deltodesco's name on it. ;-)

lightning

Real Member

Registered: 2007-02-26

Posts: 2,060

Re: solve it please

uhhhhhhhh

i'm just gonna listen + learn

   

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ksa-boy

Guest

Re: solve it please

thanks alot alot luca-deltodesco  ... my problem was in solving the two equations with each other
and dont worry Maelwys  i'll write his name (a):D