logs

[__SB]

f(x)= 3 + 4e^(-x)

ii) Find an expression for f^-1(x), and state the domain and range of f^-1

Can anybody see where I’m going wrong in my working?
I see how you get the correct answer if you rearrange beforetaking natural logs but I’m interested as to finding out why it doesn’t work beforehand.Any help will be greatly appreciated, cheers.

 

[Ishuda]

f(x)= 3 + 4e^(-x)

ii) Find an expression for f^-1(x), and state the domain and range of f^-1

Can anybody see where I’m going wrong in my working?
I see how you get the correct answer if you rearrange beforetaking natural logs but I’m interested as to finding out why it doesn’t work beforehand.Any help will be greatly appreciated, cheers.

The image is turned on its side and I find it somewhat difficult to read but, if I am seeing correctly, you have something like
2 = 1 + 1
ln(2) = ln(1) + ln(1)

Logarithms do not distribute over addition. The proper way to do that is
ln(2) = ln (1 + 1)
or maybe
ln(2 - 1) = ln(1)

Again, if I am seeing correctly, the latter is the type of thing that you mean by "if you rearrange before taking natural logs ..."

 

[__SB]

The image is turned on its side and I find it somewhat difficult to read but, if I am seeing correctly, you have something like
2 = 1 + 1
ln(2) = ln(1) + ln(1)

Logarithms do not distribute over addition. The proper way to do that is
ln(2) = ln (1 + 1)
or maybe
ln(2 - 1) = ln(1)

Again, if I am seeing correctly, the latter is the type of thing that you mean by "if you rearrange before taking natural logs ..."

Cheers for the explanation- never realised that but it’sobvious now you’ve pointed it out. Sorry for the long reply by the way, I hadto wait for my thread to be approved due to it containing a picture and I forgotto check back, sorry, didn’t want to appear rude!