Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. e^(1−5x)=793

Key Concepts

Exponential Equations

Exponential equations are mathematical expressions in which variables appear as exponents. To solve these equations, one typically isolates the exponential term and applies logarithmic functions to both sides. This allows for the conversion of the exponential form into a linear form, making it easier to solve for the variable.

Natural and Common Logarithms

Natural logarithms (ln) and common logarithms (log) are two types of logarithmic functions. The natural logarithm is based on the constant e (approximately 2.718), while the common logarithm is based on 10. Understanding how to use these logarithms is crucial for solving exponential equations, as they help to simplify the equation and isolate the variable.

Calculator Usage for Approximations

Using a calculator to obtain decimal approximations is an essential skill in solving exponential equations. After isolating the variable and applying logarithms, the resulting expression often requires numerical evaluation. Calculators can provide quick and accurate decimal approximations, which are particularly useful for presenting solutions in a clear and concise manner.