# Formulas For Logarithm

## Formulas for Logarithms

When  the power of a number must be raised in order to get some other number known as Logarithm. ### Formulas for Logarithm:-

• Definition & Logarithm Formulas:

Logarithms are the power to which a number is raised to achieve some other number.

• Logarithms is of 2 types:-
• Common logarithm
• Natural logarithm.
• Common Logarithm-

Logarithm with base 10 is Common logarithm.

It is expressed as log10 X,  and if any expression is not given with the base, then the base 10 is considered.

• Natural Logarithm-

Logarithm with base e is Natural Logarithm.

It is expressed as logX.

• Very Important: If the base is not provided, then always remember to consider base as 10.

### Formulas for Logarithm

• logx X= 1
• loga 1= 0
• a loglogax =X
• logax =  $\frac{1}{log_x a} \$
• loga(x p) = p(log ax)
• loga x = $\frac{log_{10} X}{log_{10} a} \$
• loga$\frac{x}{y} \$= loga X- loga Y
• loga (xy)= logaX+ logaY

### Value of log(2 to 10): Remember

• Log 2 = 0.301
• Log 3 = 0.477= 0.48
• Log 4 = 0.60
• Log 5 = 0.698 = 0.7
• Log 6 = 0.778 = 0.78
• Log 7 = 0.845 = 0.85
• Log 8 = 0.90
• Log 9 = 0.954= 0.96
• Log 10 = 1

### Logarithm Formulas (Antilog):

• An antilog is the inverse function of a logarithm.
log(b) x = y means that antilog (b) y = x.
• The best way to understand any problem is by having a look at the Solved Example.
• We are going to do the same here, and we are going to understand the Antilog problem by Solved Example.

Question:   Calculate the antilog of 3.6552

Solution:     As we know that antilog is the inverse of the logarithm. so, it is clear that we are going to find the number whose logarithm is 3.6552

From the antilog table,  we would find the value corresponding to the row 65 and column 5 is 4508.

The mean difference column for the value 2 is 2.

Adding these two values, we have 4518 + 2 = 4520. The decimal point is placed in 3 + 1 = 4 digits from the left. So, antilog 3.6552 = 4520.0

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