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# Which of the following shows the extraneous solution to the logarithmic equation below? log3(18x^3)-log3(2x)=log3(144) x=-16 x=-8 x=-4 x=-2

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We can simplify this equation using logaritmic rules. log x-logb = log(x/b)of the equation becomes.log3((18x^3)/(2x)) = log3(144) orlog3(9x^2) = log3(144)for x= -4, we observe that the left-hand side is equal to right sidelog3(9*(-4)^2) = log3(144), but if you put the value of x=4, in the beginning you will get log3(18(-4)^3), which is the log of negative value which is impossible. That is why x=-4 is extraneous solution.