# logarithm

• May 6th 2007, 10:45 PM
papercut06
logarithm
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, 10:53 PM
Jhevon
Quote:

Originally Posted by papercut06
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

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, 11:55 PM
earboth
Quote:

Originally Posted by papercut06
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

Hello,

I used a slightly different way than Jhevon. I've attached a screenshot of my calculations:
• May 7th 2007, 12:09 AM
Jhevon
Quote:

Originally Posted by earboth
Hello,

I used a slightly different way than Jhevon. I've attached a screenshot of my calculations:

that's a nice way earboth, but i don't think you should have that 2^log(5) at the front, the last line should start with the 5^log(2) i believe