Solve the logarithmic equation
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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.

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 .

good luck on your studies! : )

david edward.