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exponents

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Senior Manager
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Joined: 11 May 2004
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exponents [#permalink] New post 05 Nov 2005, 13:19
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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 [#permalink] New post 05 Nov 2005, 13:41
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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 [#permalink] New post 06 Nov 2005, 00:48
I meant can you please explain your steps :)
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Re: exponents [#permalink] New post 06 Nov 2005, 06:06
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
Re: exponents   [#permalink] 06 Nov 2005, 06:06
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