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Re: Variable Exponent Problem [#permalink]
26 Jun 2008, 22:22

thanks but sadly I am still confused! I am having trouble understanding what exactly you did to the 125,000 (i believe it was a mistake you left off a zero but I am confused aside from that)

I get why you did 5^[(2x)3] but am have trouble breaking out the other side!

Re: Variable Exponent Problem [#permalink]
26 Jun 2008, 23:39

1

This post received KUDOS

hardaway7 wrote:

thanks but sadly I am still confused! I am having trouble understanding what exactly you did to the 125,000 (i believe it was a mistake you left off a zero but I am confused aside from that)

I get why you did 5^[(2x)3] but am have trouble breaking out the other side!

Thanks so much for your help

5^6x = (5^2x)^3=12500

so, now, you will have to take the 1/3rd power of both sides.

(5^6x)^(1/3) = (12500)^(1/3)

(5^6x)^(1/3) = 5^(2x) and 12500 = 125*100 = (5^3)*(100)

so (12500)^(1/3) = [(5^3)^(1/3)]*(100)^(1/3) = 5*[(100)^(1/3)]

so 5^(2x) = 5*[(100)^(1/3)]

now, 5^(2x-1) = (5^2x)/5

substituting the value of 5^2x in the above equation :

Re: Variable Exponent Problem [#permalink]
27 Jun 2008, 15:39

believe it or not guys, i just solved this problem off the top of my head within 30 seconds without even using a scratch paper!!

ok, 5^6x=125,000

5^(2x-1)=?

we know that if we find the cube root of (5^6x), we will have 5^2x. If you had memorized your cubes, you would have known that 5^3 is equal to 125. So you automatically know that the cube root of 125,000 is 5,000. Also, 5^(2x-1) means 5^2x / 5, therefore: 5000 / 5 = 1000 is our answer.

Re: Variable Exponent Problem [#permalink]
27 Jun 2008, 18:48

and yet, your modesty yielded a wrong answer.

tarek99 wrote:

believe it or not guys, i just solved this problem off the top of my head within 30 seconds without even using a scratch paper!!

ok, 5^6x=125,000

5^(2x-1)=?

we know that if we find the cube root of (5^6x), we will have 5^2x. If you had memorized your cubes, you would have known that 5^3 is equal to 125. So you automatically know that the cube root of 125,000 is 5,000. Also, 5^(2x-1) means 5^2x / 5, therefore: 5000 / 5 = 1000 is our answer.

Re: Variable Exponent Problem [#permalink]
27 Jun 2008, 20:23

tarek99 wrote:

the cube root of 125,000 is 5,000.

here is what went wrong.

I do these mistakes all the time, on an average 3 - 5 times in a test. and I'm hoping on the GMAT day, all such errors will be in experimental questions...

Re: Variable Exponent Problem [#permalink]
11 Jul 2008, 16:22

gmatnub wrote:

and yet, your modesty yielded a wrong answer.

tarek99 wrote:

believe it or not guys, i just solved this problem off the top of my head within 30 seconds without even using a scratch paper!!

ok, 5^6x=125,000

5^(2x-1)=?

we know that if we find the cube root of (5^6x), we will have 5^2x. If you had memorized your cubes, you would have known that 5^3 is equal to 125. So you automatically know that the cube root of 125,000 is 5,000. Also, 5^(2x-1) means 5^2x / 5, therefore: 5000 / 5 = 1000 is our answer.

Sorry! the cube root of 125,000 is simply 50! so when you divide 50 /5, you will have 10.

gmatclubot

Re: Variable Exponent Problem
[#permalink]
11 Jul 2008, 16:22