SOLVING LOGARITHMIC EQUATIONS
SOLVING LOGARITHMIC EQUATIONS
Note:
If you would like an in-depth review of logarithms, the rules of logarithms, logarithmic functions and logarithmic equations, click on logarithmic function.
Solve for x in the following equation.
Example 1:
Note that the domain of 
is the set of real numbers greater than
zero because you cannot take the log of zero or a negative number
Isolate the logarithmic term.
Convert the logarithmic equation to an exponential equation.
The exact answer is 
and the approximate value 
Check the answer by substituting 2.46301869964 in the
original equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the correct
answer.
You can also check your answer by graphing 
(formed by subtracting the right side of the original equation from
the left side). Look to see where the graph crosses the x-axis; that will be
the real solution. Note that the graph crosses the x-axis at 2.46301869964
. This means that 2.46301869964 is the real solution.
If you would like to work another example, click on Example
If you would like to test yourself by working some problems similar to this
example, click on Problem
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