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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
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
```

```
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/
```
Associated Topics:
High School Logs

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