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Find the solution set of the equation:
Solution:
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.