Logarithmic Functions

Logarithmic Functions

The logarithm function is defined by the equation 
    "logarithm of x base a"
    domain{x|x>0}  range: R
"y is the number to which a must be raised to give x"

Logarithm is another name for exponent

Note:
When a=10 y=log_ax = log₁₀x = logx (Common or Briggsian Logarithm)
When a=e =2.72, y = log_ex = lnx (Natural or Napierian Logarithm)

The Basic Properties of Logs

1. log_b(xy) = log_bx + log_by.

2. log_b(x/y) = log_bx - log_by.

3. log_b(xⁿ) = n log_bx.               

4. log_bx = log_ax / log_ab.          




Examples: