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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 

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


Logarithms are just another way of expressing exponents.  

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

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   
Associated Topics:
High School Logs

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