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## Answers ( )

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

x. 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

x= 6:Hence,

x= 6 is indeed a solution.Checking

x= -3:Since the second term is undefined,

x= -3 is not a solution.Therefore, our only solution is

x= 6.Answer:x = 6

Step-by-step explanation:The given logarithmic equation is ,

We can notice that the bases of both logarithm is same . So we can use a property of log as ,

So we can simplify the LHS and write it as ,

Now simplify out x(2x – 6 ) . We get ,

Again , we know that ,

Using this we have ,

Now simplify the quadratic equation ,

Since logarithms are not defined for negative numbers or zero , therefore ,

Therefore the equation is not defined at x = -3 . Hence the possible value of x is 6 .