As a data analyst apprentice, you are instructed to linearize a complex geometric growth model represented by the logarithmic expression $\log_3\sqrt[3]{\frac{x^2}{5yz}}$. To properly encode this model into the company's legacy database system, you must expand the expression step-by-step using logarithm properties. Arrange the steps of this logarithmic expansion in the correct chronological order.

As a documentation specialist for a technical engineering firm, you are tasked with verifying the mathematical proofs used in a system manual. One section involves expanding the complex logarithmic expression $\log_3\sqrt[3]{\frac{x^2}{5yz}}$. To ensure the manual is accurate, match each specific expansion action described below with the property of logarithms or algebraic rule that justifies it.

You are a junior data analyst for a renewable energy firm tasked with simplifying a formula used to calculate solar efficiency: $\log_3\sqrt[3]{\frac{x^2}{5yz}}$. After you rewrite the cube root as a fractional exponent, which property of logarithms must be applied next to move that exponent to the front of the expression?

As a quality assurance intern at a software firm, you are reviewing the logic for a mathematical expansion tool. One test case involves the expression $\log_3\sqrt[3]{\frac{x^2}{5yz}}$. True or False: According to the properties of logarithms and exponents, the first step to expand this expression is to rewrite the cube root as an exponent of ${}3$.

Technical Maintenance: Formula Scaling