Logaritmewetten

A logarithm indicates how many times a base must be multiplied by itself to reach a specific number. Base 10 logarithms are usually written as 'log'.

Two important types of logarithmic laws are the product law and the quotient law.

The product law states that the logarithm of a product equals the sum of the logarithms.

For example, the logarithm of 10 times 10 is the logarithm of 100, which equals 2. According to the product rule, this equals the sum of the logarithms of 10 and 10 — both of which are 1, because the logarithm of a number to its own base is 1, giving a total of 2.

The quotient law states that the logarithm of a quotient equals the difference of the logarithms.

For example, the logarithm of 10 divided by 10 is the logarithm of 1, which equals 0 since the logarithm of 1 to any base is 0. The quotient rule shows this equals the difference between the logarithms of 10 and 10 — giving 0.

The pH scale, for instance, uses logarithms to measure acidity from hydrogen ion concentration. If the concentration is 2 times 10 to the power of negative 7 mol/L, pH is the negative logarithm of that. The product law simplifies this to 6.7.