Answer:
Step-by-step explanation:
We want to solve the equation:
Recall the property:
Hence:
Next, recall that by the definition of logarithms:
Therefore:
Solve for <em>x</em>. Simplify and distribute:
We can divide both sides by two:
Subtract 18 from both sides:
Factor:
Zero Product Property:
Solve for each case. Hence:
Next, we must check the solutions for extraneous solutions. To do so, we can simply substitute the solutions back into the original equations and examine its validity.
Checking <em>x</em> = 6:
Hence, <em>x</em> = 6 is indeed a solution.
Checking <em>x</em> = -3:
Since the second term is undefined, <em>x</em> = -3 is not a solution.
Therefore, our only solution is <em>x</em> = 6.