Solving Exponential Equations Using Logarithms

Example 10.41: Solving $5^x = 11$

Try It 10.81 and 10.82: Solving $7^x = 43$ and $8^x = 98$

Example 10.42: Solving $3e^{x+2} = 24$

Try It 10.83 and 10.84: Solving $2e^{x-2} = 18$ and $5e^{2x} = 25$

Solving an Exponential Equation by Rewriting with a Common Base

In professional fields such as finance and technology, analysts use different mathematical models to track growth and change. Which of the following represents an exponential equation?

In a professional financial model, an analyst uses the equation ${}500(1.04)^t = 1000$ to predict how many years ($t$) it will take for an investment to double. This is classified as an exponential equation because the variable $t$ is located in the exponent of the expression.

Structural Characteristics of Exponential Equations

In a professional financial report, an analyst uses the formula $V = 1000(1.05)^t$ to predict the future value of an investment over time $t$. Because the variable representing time is located in the exponent of the expression, this is specifically classified as a(n) ____ equation.

Auditing Business Growth Models