Logarithms Questions and Answers

Logarithm Questions and Answers

Common Logarithm and Natural Logarithm: 

• Common logarithm has base 10 ($b = 10$) and is denoted as $\log(x)$, while natural logarithm has base $e$ (Euler’s number) and is denoted as $\ln(x)$.

Logarithm Rules:

• Product Rule:  log_{b}\left ( xy \right )= log_{b}\left ( x \right )+log_{b}\left ( y \right )
• Quotient Rule: log_{b}\left ( \frac{x}{y} \right )=log_{b}\left ( x \right )-log_{b}\left ( y \right )
• Power Rule: log_{b}\left ( x \right )^{n}=nlog_{b}\left ( x \right )

A logarithm denote as the contradictory of power. In other terms, if we go for a logarithm of a particular value, we unknot exponentiation. Logarithm Questions and Answers are discussed below:

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

• Log₂(8) = 3
• Log₄(64) = 3
• Log₅(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