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# Logarithm Questions and Answers

# Logarithm Questions

## Definition of Logarithm

**A logarithm denote as the contradictory of power. In other terms, if we go for a logarithm of a particular value, we unknot exponentiation.**

For instance: If the base is taken as b = 3 and increase it to the power of k = 2 we get the result as 32. The result is referred as c, showed by 32 = C. The rules of exponentiation can be used to evaluate that the result is C =32 = 8.

Given an example, consider that someone inquired “2, raised to which power is equivalent to 16”? The result will be 4. It is further articulated by the logarithmic calculation, i.e. log2 (16) = 4, which is further spoken as “log base two of sixteen is four.”

**Logarithm form**

Log_{2}(8) = 3

Log_{4}(64) = 3

Log_{5}(25) = 2

**Exponential form**

2^3= 8

4^3= 64

5^2= 25

Generalizing the examples above leads us to the formal definition of a logarithm.

Logb (a) =c ↔ bc =a

Both the equations define the similar link where:

‘b’ is considered as the base,

c is considered as the exponent

a is considered as the argument

**There are certain laws of logarithm which you should know in order to solve the questions in an appropriate way. **

- Law 1: log A + log B = log AB That is, log of product = sum of logs
- Law 2: log A/b = log A- log B That is, log of quotient = difference of logs
- Law 3:
log A
^{n}= n log A

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