Math Is Fun Forum

Avva

Member

Registered: 2009-02-25

Posts: 41

log

loglog(x^2-7x+15)=123

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: log

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: log

Hi Avva;

Soroban has raised a legitimate concern. I also am assuming that by log you mean the common logartihm to the base 10 and not the natural one to the base e.

This is from a paper i read a while back written either by Hardy or Littlewood about how to simplify tower problems.Looking at the equation:

Here is what you can do,

Since 10^(10^(123)) - 15 is essentially 10^(10^(123))  we can drop the 15 and get.

Again since 7x is so much smaller than x^2 when x is large we can drop the 7x without affecting the answer significantly. What we are now trying to some is:

Since 10 ^ 123 can be factored into 2^123 * 5^123 we can factor it a little more into.

Keep in mind that the equality sign here is being used in the loosest possible manner. The neglected terms are so small you couldn't include them even if you wanted to.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.