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exponents

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desiguy
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exponents [#permalink] New post   05 Nov 2005, 14:19
x=10^100, x^x=10^k
k=?

10^5
10^102
10^99
10^200
10^98


Please show your calcs...



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nakib77
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Re: exponents [#permalink] New post   05 Nov 2005, 14:41
10^102
is my answer

x=10^100, x^x=10^k

so (10^100)^10^100 = 10^k

or 10 ^10^(2+10^100) = 10^k

so we can solve it for k= 10^102
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parikshat
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Re: exponents [#permalink] New post   06 Nov 2005, 01:48
I meant can you please explain your steps :)
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sandalphon
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Re: exponents [#permalink] New post   06 Nov 2005, 07:06
desiguy wrote:
x=10^100, x^x=10^k
k=?

10^5
10^102
10^99
10^200
10^98


Please show your calcs...


That one is easy.

Fill in the first equation with the content of the second. You get:

(10^100)^(10^100) = 10^k

The crux is the following. On both sides of the equation you have 10 as the base, you must now find out k. Simplify:

(10^10^2) ^ (10^100) = 10^k

Now you can multiply the exponents.

10^(10^2 * 10^100) = 10 ^k

Focus on the equation inside the parentheses. Since you have the same base you can add 2 and 100. The result is 10^102




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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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Thank you for understanding, and happy exploring!
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gmatclubot
Re: exponents [#permalink]
06 Nov 2005, 07:06
Moderator:
yashikaaggarwal
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