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Verified Answer :

Lampa20

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.

abidemiokin

The value that shows the extraneous solution to the logarithmic equation below is x = -4

Extraneous solutions to a system of equation

Given the logarithmic function expressed as:

log3(18x^3)-log3(2x)=log3(144)

This can also be written as:

log3(18x^3/2x)  = log3(144)
log3 (9x^2) -= log3 (144)

Cancel out the log function to have:

9x^2 = 144

Divide both sides by 9

x^2 = 144/9
x^2 = 16

x = ±4

Hence the value that shows the extraneous solution to the logarithmic equation below is x = -4

Learn more on extraneous solution here:https://brainly.com/question/2959656

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