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^(5x−3) − 2=10,476

Key Concepts

Exponential Equations

Exponential equations are mathematical expressions where a variable appears in the exponent. To solve these equations, one typically isolates the exponential term and then applies logarithmic functions to both sides. This process allows for the transformation of the equation into a linear form, making it easier to solve for the variable.

Logarithms

Logarithms are the inverse operations of exponentiation, allowing us to solve for exponents in equations. The natural logarithm (ln) and common logarithm (log) are two types used frequently in algebra. When solving exponential equations, taking the logarithm of both sides helps to bring down the exponent, facilitating the isolation of the variable.

Calculator Use for Approximations

Using a calculator to obtain decimal approximations is essential in solving exponential equations, especially when the solutions involve logarithms. Most scientific calculators can compute natural and common logarithms, providing numerical values that can be rounded to a specified number of decimal places. This step is crucial for presenting solutions in a practical format.