Question

Which of the following shows the extraneous solution to the logarithmic equation below?

Answer 1

We can simplify this equation using logaritmic rules. logx-logb  = log(x/b)

than our equation becomes.
log3((18x^3)/(2x)) = log3(144)   or
log3(9x^2) = log3(144)

for x= -4 we get that left side is equal to right side
log3(9*(-4)^2) = log3(144)

but if you put that value of x=-4 in start you will get log3(18(-4)^3) which is log of negative value which is imposible. That is why x=-4 is extraneous solution. 

Answer 2

The answer is C. x=-4

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