LOGARITHMIC AND EXPONENTIAL FUNCTIONS
Exponential functions
Inverse relations
Properties of Logarithms
Exponential and logarithmic equations
THE LOGARITHMIC FUNCTION WITH BASE b is the function
y = log b x .
b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). The function is defined for all x > 0. Here is its graph for any base b .
Note the following:
For any base, the x -intercept is 1.
The function is defined only for positive values of x
The range of the function is all real numbers.
The negative y -axis is a vertical asymptote
Translation of axes . Here is the graph of the natural logarithm , y = ln x
And here is the graph of y = ln ( x − 2) -- which is its translation 2 units to the right.
The x -intercept has moved from 1 to 3. And the vertical asymptote has moved from 0 to 2.
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