Question 1138795
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There is certainly no need to get into 4th degree polynomial equations in solving this problem.<br>
With only a little bit of experience, when you see an equation involving a log base 16 and a log base 4, you should recognize that almost certainly you will want to change the equation into an equation involving only base 4 logs or only base 16 logs.<br>
In this problem, log of x base 16 is half as big as log base x of 4, because the base 16 is the square of the base 4.  So the left side of the equation, 4 times log base 16 of x, converts to 2 times log base 4 of x, and the solution is far easier because you end up with a quadratic equation instead of a quartic.<br>
So go the path shown by tutor @ikleyn....