Hi, can someone help with this

How do i prove that the following statement is true?

2^log(5) is equal to 5^log(2)

Thanks a lot

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- May 6th 2007, 09:45 PMpapercut06logarithm
Hi, can someone help with this

How do i prove that the following statement is true?

2^log(5) is equal to 5^log(2)

Thanks a lot - May 6th 2007, 09:53 PMJhevon
let 2^log(5) = x

take log of both sides, we get:

log[2^log(5)] = log(x)

=> log(5)*log(2) = log(x) ................since log(a^b) = blog(a)

=> log(2)*log(5) = log(x)

=> log(5)^log(2) = log(x) ................since blog(a) = log(a^b)

now we can drop the logs, we get

5^log(2) = x

but 2^log(5) = x

=> 5^log(2) = 2^log(5)

if there's anything you don't get, say so - May 6th 2007, 10:55 PMearboth
- May 6th 2007, 11:09 PMJhevon