The "solution" in the post by @CubeyThePenguin is TOTALLY WRONG.
It has nothing in common with the correct solution.
Introduce new variable x = .
Then the equation takes the form
x^4 + x^3 - 243 = 0.
The roots of the polynomial (approximate values) are:
= 3.72008
= −4.22409
= −0.248 + 3.9246i
= −0.248 − 3.9246i
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas.
Of these roots for x = , for us only the positive real value
= 3.72008
make sense.
Then from = 3.72008 you have = = 0.26881.
And THEREFORE, m*log(3) = log(0.26881), which implies
m = = -1.19583 (approximate). ANSWER
