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Hey, in need of a helping hand on this function Q! :) watch

1. Hiya, so the Q is:
f(x)=4-ln3x
g(x)=e2-x
show that fg(x)=x+a-lnb where a and b are integers to be found
So fg(x)=4-ln3(e2-x)
everything past this point is me just wildly guessing:
4-ln(3e2/ex) -> 4-(ln3e2-lnex)
4-ln3e2+x
=x+4-ln3e^2
This looks right up to here, then how do I simplify ln3e^2 to an integer?
ln3e2=ln3+lne2=ln3+2...?
2. (Original post by Exephy)
Hiya, so the Q is:
f(x)=4-ln3x
g(x)=e2-x
show that fg(x)=x+a-lnb where a and b are integers to be found
So fg(x)=4-ln3(e2-x)
everything past this point is me just wildly guessing:
4-ln(3e2/ex) -> 4-(ln3e2-lnex)
4-ln3e2+x
=x+4-ln3e^2
This looks right up to here, then how do I simplify ln3e^2 to an integer?
ln3e2=ln3+lne2=ln3+2...?
Y = In x is the inverse function (log base e) of e^y , so if y = ln (e^x) then y = x as the function is basically undone by its inverse.
3. (Original post by kkboyk)
Y = In x is the inverse function (log base e) of e^y , so if y = ln (e^x) then y = x as the function is basically undone by its inverse.
I know, haha. But how does that help me here?
4. (Original post by Exephy)
I know, haha. But how does that help me here?
You basically apply that to any natural log function with an exponential function within it in your question. E.g. 3ln(e^(2-x)) = 3 (2-x)
5. (Original post by kkboyk)
You basically apply that to any natural log function with an exponential function within it in your question. E.g. 3ln(e^(2-x)) = 3 (2-x)
the problem is that the form the answer wants it in requires ln to be there :/
6. (Original post by Exephy)
Hiya, so the Q is:
f(x)=4-ln3x
g(x)=e2-x
show that fg(x)=x+a-lnb where a and b are integers to be found
So fg(x)=4-ln3(e2-x)
everything past this point is me just wildly guessing:
4-ln(3e2/ex) -> 4-(ln3e2-lnex)
4-ln3e2+x
=x+4-ln3e^2
This looks right up to here, then how do I simplify ln3e^2 to an integer?
ln3e2=ln3+lne2=ln3+2...?
You don't want ln(3e^2) to be an integer!

Remember the question requires the final answer to have a logarithm in it. So all you need are 2 basic rules:

ln(ab) = ln a + ln b

I haven't checked all your manipulations, but these 2 rules are all you need to get through the question
7. (Original post by davros)
You don't want ln(3e^2) to be an integer!

Remember the question requires the final answer to have a logarithm in it. So all you need are 2 basic rules:

ln(ab) = ln a + ln b

I haven't checked all your manipulations, but these 2 rules are all you need to get through the question
I got it, thanks!

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