In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x = 7000

Exponential equations are mathematical expressions in which a variable appears in the exponent. 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.

Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in an equation. For example, if we have an equation of the form a^b = c, we can express it in logarithmic form as b = log_a(c). In this context, natural logarithms (ln) and common logarithms (log) are often used to simplify calculations and express solutions.

Using a calculator to obtain decimal approximations is essential when dealing with logarithmic solutions that do not yield simple rational numbers. Most scientific calculators can compute logarithms directly, providing a numerical value that can be rounded to a specified number of decimal places, which is particularly useful in practical applications and when presenting final answers.