# Log Table Elements Complete Chart PDF

## Log Table Elements

Sometimes, a numerical expression may involve multiplication, division or rational powers of large numbers. For such calculations, logarithms are very useful. They help us in making difficult calculations easy. In Chemistry, logarithm values are required in solving problems of chemical kinetics, thermodynamics, electrochemistry, etc. We shall first introduce this concept, and discuss the laws, which will have to be followed in working with logarithms, and then apply this technique to a number of problems to show how it makes difficult calculations simple.

We know that

2³ = 8, 3² = 9, 5³ = 125, 7⁰ = 1

Another way of stating the same fact is logarithm of b to base a is m.

If for a positive real number a, a # 1

we say that m is the logarithm of b to the base a.

We write this as log b = m.

In general, for a positive real number a, and a rational number m, let a” = b. where b is a real number. In other words the mth power of base a is b. a = b. published

Laws of Logarithms

In the following discussion, we shall take logarithms to any base a, (a > 0 and a # 1)

First Law: loga (mn) = logam + logan

Proof: Suppose that logam = x and logan = y

Then a m, a = n

Hence mn = a*.a = axty

It now follows from the definition of logarithms that

loga (mn) = x + y = loga m loga n

Second Law: loga (m/n) = logam – logan