If the logarithmic function is one-to-one,
its inverse exits. The inverse of a logarithmic function is
an exponential function. When you graph both the logarithmic
function and its inverse, and you also graph the line y = x,
you will note that the graphs of the logarithmic function and
the exponential function are mirror images of one another with
respect to the line y = x. If you were to fold the graph along
the line y = x and hold the paper up to a light, you would note
that the two graphs are superimposed on one another. Another
way of saying this is that a logarithmic function and its inverse
are symmetrical with respect to the line y = x.
Example 5: Find the inverse of
The base is e, the exponent is x, and the problem can be converted to the exponential function
If you graph the problem, notice that the graph is one-to-one. Therefore, we not have to restrict the domain. Notice that the domain is the set of all real numbers .
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Author: Nancy Marcus