# how to use log table to find log and anti-log to find pH and concentration???

### Asked by | 8th Dec, 2012, 09:56: PM

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The logarithm of a number has two parts the first of which is the exponent of 10, called the characteristic, and the second part is a decimal called the mantissa which is read from the log tables. The characteristic can be positive or negative. The negative characteristic is written with a bar above the number. The mantissa is always a positive decimal less than 1.

**How to find log: **

To look up a logarithm of say, 15.27, you would First work out the characteristic, in this case it is 1 Run your index finger down the left-hand column until it reaches 15 Now move it right until it is on column 2 (it should be over 1818) Using another finger, find the difference on column 7 of the differences (20) Add the difference.

So the logarithm of 15.27 is 1.1818 + 0.0020 = 1.1838

**Antilog of x is equal to 10**^{x}

For example find the antilog of 2.6992

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

Thus antilog 2.6992 = 500.2
**Calculation of concentration from pH:**

The pH is equal to the base 10 logarithm of the H^{+} concentration, multiplied by -1. If you know the pH of a solution, you can use this formula in reverse to calculate the H^{+} concentration in that solution.

For ex: calculate [H^{+}] of a solution with pH= 4.30

pH = - log [H^{+}]

4.30 = - log [H^{+}]

- 4.30 = log [H^{+}]

Divide -4.30 into 2 parts so that the first part contains the decimal places and second part the whole number.

-4.30 = 0.70 - 5 = log [H^{+}]

Find the antilog:

Antilog of 0.70 = 5.0

Antilog of -5 = 10^{-5}

Now, multiply both the antilog to get [H^{+}]:

5.0 x 10^{-5 }= [H^{+}]

So, [H^{+}] = 5.0 x 10^{-5 }M

The logarithm of a number has two parts the first of which is the exponent of 10, called the characteristic, and the second part is a decimal called the mantissa which is read from the log tables. The characteristic can be positive or negative. The negative characteristic is written with a bar above the number. The mantissa is always a positive decimal less than 1.

**How to find log: **

To look up a logarithm of say, 15.27, you would First work out the characteristic, in this case it is 1 Run your index finger down the left-hand column until it reaches 15 Now move it right until it is on column 2 (it should be over 1818) Using another finger, find the difference on column 7 of the differences (20) Add the difference.

So the logarithm of 15.27 is 1.1818 + 0.0020 = 1.1838

**Antilog of x is equal to 10 ^{x}**

For example find the antilog of 2.6992

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

**Calculation of concentration from pH:**

The pH is equal to the base 10 logarithm of the H^{+} concentration, multiplied by -1. If you know the pH of a solution, you can use this formula in reverse to calculate the H^{+} concentration in that solution.

For ex: calculate [H^{+}] of a solution with pH= 4.30

pH = - log [H^{+}]

4.30 = - log [H^{+}]

- 4.30 = log [H^{+}]

Divide -4.30 into 2 parts so that the first part contains the decimal places and second part the whole number.

-4.30 = 0.70 - 5 = log [H^{+}]

Find the antilog:

Antilog of 0.70 = 5.0

Antilog of -5 = 10^{-5}

Now, multiply both the antilog to get [H^{+}]:

5.0 x 10^{-5 }= [H^{+}]

So, [H^{+}] = 5.0 x 10^{-5 }M

### Answered by | 11th Dec, 2012, 12:12: PM

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