Let a and N be positive real numbers and let N = an. Then n is called the logarithm of N to the base a. We write this as n = loga N.

Find the value of log3 27 is

Rewrite as an equation:

log3 27 = x

Rewrite log3 27 = x in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then logb x = y is equivalent to by=x

3x=27 <=> 3x= 33 <=> x = 3

Rules of Logarithms:

The following important rules apply to logarithms.

Rule nameRule
Logarithm product rulelogb(x ∙ y) = logb(x) + logb(y)
Logarithm quotient rulelogb(x / y) = logb(x)logb(y)
Logarithm power rulelogb(x y) = y ∙ logb(x)
Logarithm base switch rulelogb(c) = 1 / logc(b)
Logarithm base change rulelogb(x) = logc(x) / logc(b)
Derivative of logarithmf (x) = logb(x)⇒ f ‘ (x) = 1 / ( x ln(b) )
Integral of logarithm∫logb(x) dx = x ∙ ( logb(x)- 1 / ln(b)) + C
Logarithm of negative numberlogb(x) is undefined when x≤ 0
Logarithm of 0logb(0) is undefined
Logarithm of 1logb(1) = 0
Logarithm of the baselogb(b) = 1
Logarithm of infinitylim logb(x) = ∞,when x→∞