
An exponential function is any function of the form:where the base=b is positive, b is not equal to 1 and x is any real number. A logarithmic function is any function of the form:
where the base=b is positive, b is not equal to 1 and x>0 . (It is read as "log, base b, of x") The logarithm is a new function obtained by trying to solve
for x. So
means the same as
. The log is equal to the exponent for the base. You can go back and forth between: Exponential form logarithmic form
And
Example 1 Write the following in logarithmic form: a.
is the same as
b.
is the same as
Example 2 Write the following in exponential form: a.
is same as
. b.
is same as
If you have missing values in a simple logarithmic expression can be evaluated by rewriting the expression in exponential form using the fact that
(When expressions have the same base then the exponents must be equal.) Example 3 Find N in each of the following:
Rewrite
9=N
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