# Thread: Trouble equating functions to check if one-to-one with natural log's

1. ## Trouble equating functions to check if one-to-one with natural log's

$e^a/(1+4e^a)=e^b/(1+4e^b)$

When I multiply each side by it's denominator I get:

$e^a+4e^a^+^b=e^b+4e^a^+^b$

hopefully I'm on the right track, then do I take the natural log of both sides? How does the natural log react in this situation with the addition? Do all the $e$'s cancel out?

2. ## Re: Trouble equating functions to check if one-to-one with natural log's

$e^a/(1+4e^a)=e^b/(1+4e^b)$

When I multiply each side by it's denominator I get:

$e^a+4e^a^+^b=e^b+4e^a^+^b$

hopefully I'm on the right track, then do I take the natural log of both sides? How does the natural log react in this situation with the addition? Do all the $e$'s cancel out?
$e^a+4e^a^+^b=e^b+4e^a^+^b$

start by subtracting $4e^{a+b}$ from both sides ...

3. ## Re: Trouble equating functions to check if one-to-one with natural log's

That was easy. Thank you. Always making it hard on myself.