The extraneous solution of the logarithmic problem
is -4.
<h3>What is Logarithm?</h3>
A log function is a way to find how much a number must be raised in order to get the desired number.
![a^c =b](https://tex.z-dn.net/?f=a%5Ec%20%3Db)
can be written as
![\rm{log_ab=c](https://tex.z-dn.net/?f=%5Crm%7Blog_ab%3Dc)
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
Solving the function using the basic logarithmic value, we get,
![\rm log_3(18x^3)-log_3(2x) = log_3 144\\\\ log_3\dfrac{(18x^3)}{(2x)} = log_3 144\\\\ log_3(9x^2)= log_3 144\\\\\text{Taking antilog}\\9x^2 = 144\\x = \sqrt{\dfrac{144}{9}}](https://tex.z-dn.net/?f=%5Crm%20log_3%2818x%5E3%29-log_3%282x%29%20%3D%20log_3%20144%5C%5C%5C%5C%20log_3%5Cdfrac%7B%2818x%5E3%29%7D%7B%282x%29%7D%20%3D%20log_3%20144%5C%5C%5C%5C%20log_3%289x%5E2%29%3D%20log_3%20144%5C%5C%5C%5C%5Ctext%7BTaking%20antilog%7D%5C%5C9x%5E2%20%3D%20144%5C%5Cx%20%3D%20%5Csqrt%7B%5Cdfrac%7B144%7D%7B9%7D%7D)
If we solve further we will get that the value of x can be either -4 or 4, if take the value of x as -4, in the beginning then you will get log₃(18(-4)³) as the log of negative value which is impossible.
Hence, x=-4 is an extraneous solution.
Learn more about Logarithms:
brainly.com/question/7302008