Transcendental functions - The graphs of transcendental functions
Exponential and logarithmic functions are mutually inverse functions
The graph of the exponential function
The graph of the logarithmic function
Transcendental functions - The graphs of transcendental functions
· Exponential and logarithmic functions are mutually inverse functions
- Exponential function  y = ex  <=>  x = ln y,   e = 2.718281828...the base of the natural logarithm,
exponential function is inverse of the natural logarithm function, so that  eln x = x.
- Logarithmic function  y = ln x = loge x    <=>    x = e y,    where x > 0
the natural logarithm function is inverse of the exponential function, so that  ln(ex) = x.
- Exponential function  y = ax   <=>   x = loga  y,   where a > 0 and  a is not 1

 exponential function with base a is inverse of the logarithmic function, so that
- Logarithmic function y = loga x    <=>    x = a y,   where a > 0a is not 1 and x > 0
the logarithmic function with base a is inverse of the exponential function, so that  loga(ax) = x.
The graph of the exponential function  y = ax = ebxa > 0  and  b = ln a
The exponential function is inverse of the logarithmic function since its domain and the range are respectively the range and domain of the logarithmic function and
ƒ(f -1(x)) = x  that is,  ƒ(f -1(x)) = ƒ(ax) =  loga(ax) = x.
The graph of the logarithmic function  y = logaxa > 0  and  for  a = ey = logex = ln x
The logarithmic function is inverse of the exponential function since its domain and the range are respectively the range and domain of the exponential function and

College algebra contents B