As a data technician apprentice reviewing a colleague's algorithm scaling calculations, you encounter the logarithmic equation ${}2\log_5 x = \log_5 81$. To begin solving this equation, you need to bring the coefficient ${}2$ inside the logarithm so that it becomes an exponent. Which mathematical property must you recall to justify this specific first step?

A logistics analyst is verifying a shipping volume model that uses the equation ${}2\log_5 x = \log_5 81$. Match each mathematical statement generated during the solution process with the correct property or rule that justifies it.

A technical auditor is reviewing a calculation that involves the logarithmic equation ${}2\log_5 x = \log_5 81$. The audit report states that the final solution set for $x$ includes two values: ${}9$ and $-9$.

True or False: Both ${}9$ and $-9$ are valid solutions for the original logarithmic equation ${}2\log_5 x = \log_5 81$.

A marketing analyst is reviewing a budget growth model that uses the logarithmic equation ${}2\log_5 x = \log_5 81$. To determine the valid value of the variable $x$, the analyst must solve the equation step-by-step. Arrange the following mathematical steps in the correct order to find the final solution.

Quality Assurance Review of Logarithmic Scaling

An operations coordinator is verifying a resource scaling formula represented by the logarithmic equation ${}2\log_5 x = \log_5 81$. After algebraically solving the equation, the coordinator finds two potential values: 9 and -9. Because the argument of a logarithm must be strictly positive, the coordinator recognizes that the value -9 is a(n) ____ solution and must be excluded.

Identifying the Property to Set Arguments Equal