Exponents

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Fri Feb 19, 2010 1:43 pm

Hi everyone,

I have a very simple, general question but I was unsure about where to post.

Do you have to have the same bases on both sides of the equation in order to equate their exponents?

i.e. 2^x * 3^4 = 2^6

You can't conclude that x=6 right?

I'm 99.9% sure especially considering the equation 2^6 * 3^4 does not equal 2^6.

Anyway, I'll throw it out there.

Thanks!

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Source: Beat The GMAT — Problem Solving | Fri Feb 19, 2010 1:43 pm

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 19, 2010 1:48 pm

pkw209 wrote:Hi everyone,

I have a very simple, general question but I was unsure about where to post.

Do you have to have the same bases on both sides of the equation in order to equate their exponents?

i.e. 2^x * 3^4 = 2^6

You can't conclude that x=6 right?

I'm 99.9% sure especially considering the equation 2^6 * 3^4 does not equal 2^6.

Anyway, I'll throw it out there.

Thanks!

To equate the powers, the bases needs to be same.

2^x * 3^4 = 2^6

2^x = 2^6/3^4 = 64/81

There will be an x , between 0 and -1 which satisfies this equation (2^0 =1 ; 2^-1 is 0.5 ; 64/81 is in between these)

You have to first write 64/81 as a power of 2 to equate powers on both the sides

Always borrow money from a pessimist, he doesn't expect to be paid back.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 1:39 am

pkw209 wrote:Hi everyone,

I have a very simple, general question but I was unsure about where to post.

Do you have to have the same bases on both sides of the equation in order to equate their exponents?

i.e. 2^x * 3^4 = 2^6

You can't conclude that x=6 right?

I'm 99.9% sure especially considering the equation 2^6 * 3^4 does not equal 2^6.

Anyway, I'll throw it out there.

Thanks!

Yeah obviously if you get values like 2^x = 2^y
then only u can say that x=y ..otherwise you willl have to solve the way ajith suggested...
But I don't think in exams such difficult situation pops up as of
2^x = 64/81
in that case log vlaue would be surely given in question itself
xlog2 = log (64/81) , so if log value is given then only can solve it

though in real exams only simple eq comes... so just keep in mind if u gonna equate power u will have to keep the bas e same...

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