As a data analyst evaluating the exponential growth of user traffic, you need to approximate the value of $\log_7 125$. Since your standard workplace calculator only computes common logarithms (base 10), you must recall the Change-of-Base Formula. Which of the following expressions should you enter into your calculator?

A quality control inspector is evaluating a batch of materials and needs to approximate the value of $\log_{3} 20$ using a handheld calculator. Since the device only has a common logarithm (base 10) button, the inspector decides to enter the expression $\frac{\log 3}{\log 20}$ to find the result. Is this a correct application of the Change-of-Base Formula?

An environmental technician is measuring light intensity and needs to approximate the value of $\log_{4} 35$ using a handheld calculator that only provides common logarithms (base 10). To apply the Change-of-Base Formula correctly, match each component of the original expression with its correct placement in the resulting conversion ratio $\frac{\log 35}{\log 4}$.

Logarithmic Conversion for Investment Growth Models

As an IT capacity planner, you need to estimate the number of server nodes required for a new distributed database, which requires approximating the expression $\log_{8} 150$. Your department's standard calculator only supports common logarithms (base ${}10$). Arrange the following steps in the correct sequence to evaluate this logarithm using the Change-of-Base Formula.

A junior marketing analyst is using a logarithmic model to analyze customer acquisition growth. To calculate a key growth metric, they need to evaluate the expression $\log_{5} 24$ using a standard office calculator that only computes common logarithms (base 10). According to the Change-of-Base Formula, this expression can be rewritten as a ratio of two common logarithms: $\frac{\log 24}{\log x}$. To evaluate the expression correctly, the value of $x$ must be ____.

Logarithmic Conversion for Warehouse Scaling