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Logarithmic Functions

Logarithms with integer bases

Let n>1 be an integer. The function lognx, which is read the "logarithm (base n) of x" or the "base n logarithm of x" is the inverse of the function fx=nx. Thus, b=na exactly when a=lognb. The domain of lognx is the set of positive numbers. The range of lognx is all numbers.

A logarithm is an exponent: lognb is the power to which you raise n to obtain the value b. Mathematically, nlognb=b.

Explore how logbx relates to bx

Use the slider below the graph to change the values of b.  Explore the graphs of the logarithmic function y = logbx and its corresponding exponential function y=bx as you vary the integer b from 2 to 10.


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