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 name | Rule |
---|---|
Logarithm product rule | logb(x ∙ y) = logb(x) + logb(y) |
Logarithm quotient rule | logb(x / y) = logb(x) – logb(y) |
Logarithm power rule | logb(x y) = y ∙ logb(x) |
Logarithm base switch rule | logb(c) = 1 / logc(b) |
Logarithm base change rule | logb(x) = logc(x) / logc(b) |
Derivative of logarithm | f (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 number | logb(x) is undefined when x≤ 0 |
Logarithm of 0 | logb(0) is undefined |
Logarithm of 1 | logb(1) = 0 |
Logarithm of the base | logb(b) = 1 |
Logarithm of infinity | lim logb(x) = ∞,when x→∞ |