Logarithims (-Logs) and (-)Anti-logs with Calculators

Std 5f

To find the pH of a solution you must take  -log [H+]

To find the pOH of a solution you must take  -log [OH-]

To find the [H+], you must take the (-)anti-log of the pH

To find the [OH-], you must take the (-)anti-log of the pOH

(For a more complete explanation of this see

Most calculators (including the TI-30Xa and the Casio fx-250HC):

1.         If the pH = 3.5   and you are asked to find the [H+]     (this is calculating an anti-log)

Enter  3.5     (or any other pH you may be given)

Press   +/-   key   (this reverses the sign)

Press    10x    key    (pressing 2nd key and then pressing the log key)

Ans   0.000316   or    3.16 x 10-4

2.         If the [H+] = 3.16  x  10-4  and you are asked to find the pH    (this is calculating a -LOG).     The TI-30Xa and Casio fx-250HC are the same except where indicated.

Enter  3.16          (  the 3 significant digits of the  [H+]  )

a.   on the  TI   press   EE  key

b.   on the Casio  press the  EXP key

Press   +/-  key   (this reverses the sign of the exponent you will enter)

Enter   4        (this is the negative exponent of 10 in the [H+]  )

Press   LOG  key   (this actually calculates the LOG  of the [H+]  you enter)

Press    +/-  key  (this makes the LOG calculated a – LOG  )

Ans   3.5

3.         If the [H+] = 3.16  x  10-4  and you are asked to find the pH  (same problem as #2 above, but we will now use a different method)          (this is calculating a -LOG)

The TI-30Xa and Casio fx-250HC are the same for all of these operations.

Enter  3.16             (  the 3 significant digits of the  [H+]  )

Press   X  key     (the times key)

Enter  10

Press   xy    key    (which may be labeled as the yx key, or xy or yx.  This allows

you put the next number entered as the exponent of 10)

Enter  4        (this is the negative exponent of 10 in the [H+]  )

Press   +/-  key   (this makes the sign of the exponent you entered negative)

Press   =  key

Press   LOG  key

Ans   pH = 3.5

Only use this method if you really like it, otherwise, stick with #2 above.
Doing these same calculations on a Graphing Calculator  like the  -  TI-85.

All calculators that have left-right, up-down keys usually use this logic.  The models that I have identified so far that use this logic are:

Casio fx-115MS, Casio fx-300MS  and Casio fx-991s

Sharp EL-531V, Sharp 520W, and Sharp EL-531;  but for Sharp EL-500L – close but  not not exact, work with it a little and/or see me)

TI 30X IIS  (Texas Instruments)

Hp  30S    (Hewlett Packard)

1.         If the pH = 3.5   and you are asked to find the [H+]  (this is calculating the -anti-log)

Press  2nd  key      (this acts like a shift key)

Press  LOG  key   (note:  LOG is changed to function as 10x , opposite of the log)

Press   (-)  key  (this changes the next number entered to be negative)

Enter   3.5   (or other pH you are trying to find)

Press   Enter  key  (this will complete the calculation and give you the concentration)

Ans   you will see 3.16 E 4  displayed,  which is the same as 3.16 x 10-4

2.         If the [H+] = 3.16  x  10-4  and you are asked to find the pH   (this is calculating a -LOG)

Press   (-)  key  (this changes the next number entered to a negative)

Press  LOG  key    (this establishes that whatever is entered next, the calculator will calculate the –LOG of the number)

Press   (  key   (this make the calculator figure everything inside the ( before it takes the log of the numbers)

Enter   3.16    (the three significant figures from the [H+]  )

Press   EE  key   (the calculator now assumes you want to enter a power of 10 next and multiply it by 3.16.   The E will now be displayed)

Press   (-)  key   (this will make the next number entered into a negative number)

Enter   4    ) key       (this number will be used as the negative exponent of 10)

Press   ENTER (or ANS)  key    (this will now allow the calculator to calculate the –LOG of your [H+]  )

Ans   pH =  3.5

NOTE:   after you are done above, with calculations where you are not in perfect scientific notation  (ex   53.2 x 10-23)  press the = key and it will be adjusted to scientific notation of 5.32 x 10-22  .

Exponents of 10 and Scientific Notation on Casio and TI

This where we take a number that is in exponents of 10 and change it into Scientific Notation and then, if we want, easily change it into a decimal.

1.  Put the number   85.3 x 10-5    into scientific notation and then into decimal form

First we change the exponent to a decimal form:

1.   Enter  85.3  then:

a.    on the  Casio  press the  EXP key  (allows entry of exponent)

b.    on the  TI  press the EE key (allows entry of exponent)

2.   Press the   +/- key   and then enter the exponent   5  (this enters the exponent as a – )

3.   When you press the  = key  the number will appear in decimal form.  (0.000853)

## 4.   To put the number into scientific notation:

a.   on the  Casio  press the  MODE key  and then number  9  (scientific notation)

b.   on the  TI  press the  2nd  key and then the number  5  (scientific notation)

On either calculator the number will now show in proper scientific notation

Ans:   8.53 x 10-4

2.  Change the number 8.53 x 10-4  back to a decimal:

a.   on the  Casio  , press MODE key and then the  number  9 again

b.   on the  TI  press the 2nd key  and then the number 4

On either calculator the number will not show in decimal form.

Ans:   0.000853