Logarithms help

Hi I just had a small question which i'm confused about if someone could help me please:

So on the disk it says
e to the power of lnk = k

why is this? I dont understand how e^lnk can be simplified to k?

Thank you!

'Ln' is the inverse function of 'e'.

So when f(x) = ln(x)
f^-1(x) = e^x and visa versa

This means ln(e^x) = x and e^ln(x) = x

oh i see thank you!

Hi I just had a small question which i'm confused about if someone could help me please:

So on the disk it says
e to the power of lnk = k

why is this? I dont understand how e^lnk can be simplified to k?

Thank you!

$\ln k = \log_e k$ is the power that you need to raise e by to get k.

So $e^{\ln k}$ is:

e to the power of (the power you need to raise e by to get k). If you think about for this a while you'll see that this must be equal to k.

In terms of functions, if $f(x)=\ln x$ then $f^{-1}(x)=e^x$ so $e^{\ln k} = f^{-1}f(k)$. If you put k through a function followed by its inverse then you'll get back to k.

Here's another explanation using log laws. And reading through the whole of that thread might be useful if you're still unsure.

EDIT : Too late!

$\ln k = \log_e k$ is the power that you need to raise e by to get k.

So $e^{\ln k}$ is:

e to the power of (the power you need to raise e by to get k). If you think about for this a while you'll see that this must be equal to k.

In terms of functions, if $f(x)=\ln x$ then $f^{-1}(x)=e^x$ so $e^{\ln k} = f^{-1}f(k)$. If you put k through a function followed by its inverse then you'll get back to k.

Here's another explanation using log laws. And reading through the whole of that thread might be useful if you're still unsure.

EDIT : Too late!

Would $\ln k \equiv \log_e k$ be more appropriate than $\ln k = \log_e k?$