Find an m ∈ R such that m ≤ (log10⁡(x) )^2 - log10⁡(∛x)/4, Find the Range Problem

A partial derivation of the important complete the square process is presented. The power law of Logarithms transforms the function into a complete the square form. ‪@MrJensenMath10‬ grade 12 presented proof of this useful simplifying result.
Find The Range Of A Quadratic Logarithmic Function. In math, range means the set of all possible numeric outputs of a function. Mark Jason Dominus presented a more general discrete math set theoretic definition of the notion of range which was not function dependent! PERL is an acronym for Practical Extraction Rubbish Lister or so says a psychotic, comedic former coding colleague of mine.
Maybe first two words in the acronym are pathologically eclectic.