1. Help Needed Understanding Logs

I am requesting help understanding natural logs. I understand that if you have lets say

ln a = b

It can be rewritten as

a = e^b

What I would like to know is if there is any way I can simply a function with natural logs in it,

So if I had any function lets say

ln x = 10 - .5 ln A + .75 ln B - 1 ln C

Is there any way I could simplify that into normal terms without a long confusing jumble? If I had inputs, how do I go about solving a function like the above?

My understanding of natural logs is limited.

Thanks for any help.

2. go to the link and learn the laws of logarithms ... natural and otherwise.

Logarithms - Topics in precalculus

I am requesting help understanding natural logs. I understand that if you have lets say

ln a = b

It can be rewritten as

a = e^b

What I would like to know is if there is any way I can simply a function with natural logs in it,

So if I had any function lets say

ln x = 10 - .5 ln A + .75 ln B - 1 ln C

Is there any way I could simplify that into normal terms without a long confusing jumble? If I had inputs, how do I go about solving a function like the above?

My understanding of natural logs is limited.

Thanks for any help.
Yes, you can simplify expressions like these using the laws of logarithms.

(i) $\dsiplaystyle \log_a b = c \implies a^c = b$

(ii) $\dsiplaystyle n \log_a X = \log_a (X^n)$

(iii) $\dsiplaystyle \log_a (XY) = \log_a X + \log_a Y$

(iv) $\dsiplaystyle \log_a \frac XY = \log_a X - \log_a Y$

(v) $\dsiplaystyle \log_a b = \frac {\log_c b}{\log_c a}$

Just a few of the rules that govern logs--the most important ones in my experience. Only some of these are needed to solve the problem you mentioned.