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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 .