Try It 10.41: Evaluating $\log_{12} 144$, $\log_4 2$, and $\log_2 \frac{1}{32}$

Try It 10.42: Evaluating $\log_9 81$, $\log_8 2$, and $\log_3 \frac{1}{9}$

In a technical laboratory setting, you may be required to manually verify logarithmic data points as part of a Quality Assurance (QA) procedure. Arrange the following steps in the correct order to evaluate a logarithm by converting it into an equivalent exponential equation.

In a technical quality control procedure, an analyst must manually verify a data point recorded as $x = \log_3(243)$. To begin evaluating this value by converting it into an exponential equation, which of the following represents the correct equivalent form?

As part of a laboratory quality control process, you need to manually verify the value of the expression $\log_2(64)$. True or False: The correct first step in evaluating this logarithm by conversion is to set it equal to a variable $x$ and rewrite it as the exponential equation ${}2^x = 64$.

In a technical environment, you may need to manually verify logarithmic data points for equipment calibration. Match each procedural term with the specific mathematical action required to evaluate a logarithm by converting it into exponential form.

SOP Documentation for Manual Logarithm Verification

You are creating a standard operating procedure (SOP) for manually verifying logarithmic sensor data. The SOP states that after converting a logarithm to an exponential equation (such as changing $\log_3(81) = x$ to ${}3^x = 81$), you must rewrite the constant term, 81, as a power so that both sides share the exact same base (resulting in ${}3^x = 3^4$). Because these bases are now identical, the ____ must be equal to each other, allowing you to solve for the variable.

SOP Onboarding: Manual Verification of Logarithmic Database Logs