A logarithmic function is basically the inverse of an exponential function.
Take a >0 and a≠1. Then the inverse of the function f:RàR defined fy f(x)=ax is logax which is called as logarithm of x with base a.
Usually log10x can be written as logx.
So the definition of logarithm is as follows.
logax = y ↔ay = x.
Example:
23=8 ==> log28 = 3.
Domain and range of logarithmic function:
Since logarithmic function is the inverse function of exponential function, the range of the logarithmic function is the domain of the exponential function which is the set of all real numbers R.
Also, the domain of the logarithmic function would be the range of the exponential function which is the set of all positive real numbers.
Graph of a logarithmic function:
Let f(x) and g(x) be the logarithmic functions such that a>1 for f(x) and 0<a<1 for g(x).
From the graph we can observe that,
(1) The domain is the set of positive real numbers and range is the set of real numbers.
(2) The function increases if a>1 and decreases if 0<a<1.
(3) The function is continuous.
(4) The vertical asymptote for the graphs is y-axis.
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