Equivalence of Logarithmic and Exponential Equations

Shape of the Graph of a Logarithmic Function where $a > 1$

Point $(a, 1)$ on the Graph of a Logarithmic Function

Point $(\frac{1}{a}, -1)$ on the Graph of a Logarithmic Function

Domain of a Logarithmic Function

Range of a Logarithmic Function

Vertical Asymptote of the Graph of a Logarithmic Function

Natural Logarithmic Function

Common Logarithmic Function

Quotient Property of Logarithms

Power Property of Logarithms

Example 10.31: Using the Quotient Property of Logarithms

Try It 10.61: Writing Logarithms as a Difference of Logarithms

Try It 10.62: Applying the Quotient Property of Logarithms

Example 10.33: Expanding a Logarithm Using the Product and Power Properties

Try It 10.65: Expanding a Logarithm Using the Product and Power Properties

Try It 10.66: Expanding a Logarithm Using the Product and Power Properties

Product Property of Logarithms

Inverse Properties of Logarithms

Logarithm of 1 Property

Logarithm of the Base Property

Example 10.34: Expanding a Logarithm with a Radical

Try It 10.67: Expanding a Logarithm with a Radical

Try It 10.68: Expanding a Logarithm with a Radical

Condensing Logarithmic Expressions

Mirror Image Relationship between Logarithmic and Exponential Functions

$x$-intercept of the Graph of a Logarithmic Function

One-to-One Property of Logarithmic Equations

Shape of the Graph of a Logarithmic Function where $0 < a < 1$

$y$-intercept of the Graph of a Logarithmic Function

As a data analyst at your company, you are modeling the growth of customer acquisitions using the exponential function $f(x) = a^x$. To determine the specific timeframe needed to reach a target number of customers, you must use the logarithmic function. Match the following logarithmic terms used in your analysis with their correct mathematical definitions or requirements.

A marketing specialist is analyzing the growth of a social media campaign. The reach of the campaign is modeled by the exponential function $R = b^t$, where $R$ is the total reach and $t$ is the time in hours. To find the time $t$ required to reach a specific audience size, the specialist must use the inverse function. Which of the following is the correct logarithmic expression for $t$?

In a corporate research setting, a scientist is using the logarithmic function $f(x) = \log_a x$ to analyze experimental data. True or False: This function is formally defined as the inverse of the exponential function $f(x) = a^x$ and is defined for all real values of $x$.

Defining Logarithmic Functions for Financial Modeling

Defining Logarithmic Functions for Operational Modeling