Biology Logarithms

Date: 04/01/99 at 12:38:46
From: Shekman007
Subject: Biology Logarithms

On a practice Sat II for Biology, I saw a problem that read: The Ph of 
an acidic pond is 5. What is the hydrogen ion concentration (moles per 
liter)? 

I did not know how to solve this. In the answer key it said that:
Ph = -log (hydrogen ion concentration)

The answer was .00001. Thus, 5 = -log (.00001). 

I do not understand how to get this answer using logarithms. Can you 
please explain it to me in very simple terms, being that I do not know 
anything about logarithms?

Date: 04/07/99 at 11:53:03
From: Doctor Nbrooke
Subject: Re: Biology Logarithms

Hello,

Logarithms are just another way of expressing exponents.  

Here is an entry in the Dr. Math archives to show just how logarithms 
work: 

   http://mathforum.org/dr.math/problems/charley.html   

Read the definition of Log by Dr. Ken and then come back here.

We'll take the formula that you started with (pH = -log([H+])) and 
work to the answer (solve for [H+]).

pH    = -log([H+])           Given.
pH    = log([H+]^(-1))       Since logarithms are like exponents, 
                             when you multiply a log by something, 
                             you can just move it to the inside of 
                             the log as an exponent. 
10^pH = 10^log([H+]^(-1))    Take each side to tenth power.
10^pH = [H+]^(-1)            Since "log" is just another notation for 
                             "log base 10", when you raise a log to 
                             the tenth power, the log cancels out.
[H+] = 10^(-pH)              Take the reciprocal of both sides.

That is the general form.  To answer your specific question, 
 
     5       = -log([H+])
     5       = log([H+]^(-1))
     10^5    = [H+]^(-1)
     10^(-5) = [H+]
     [H+]    = .00001 mol/L

- Doctor Nbrooke, The Math Forum
  http://mathforum.org/dr.math/