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Saturday, December 22, 2012

Solving Logarithmic Equation

Category: Algebra

"Published in Newark, California, USA"

Find the solution set of the equation:


The first thing that we have to do is to transpose the constant at the right side of the equation as follows

Since the left side of the equation have the same base which is x, then we can combine and apply the laws of logarithm as follows

Take the inverse logarithm on both sides of the equation to the base x as follows

The roots of the equation are: x = 3 and x = -1.

Next, check the roots of the equation by substituting the value of x to the given equation as follows

If x = 3, then

                        x = 3 is the root of the equation

If x = -1, then

                       x = -1 is an extraneous root

Therefore, the answer is x = 3