In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log0.1 17

Key Concepts

Logarithms

Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in equations of the form b^x = y. The logarithm log_b(y) answers the question: to what power must the base b be raised to obtain y? Understanding logarithms is essential for manipulating and solving equations involving exponential growth or decay.

Common and Natural Logarithms

Common logarithms (log) use base 10, while natural logarithms (ln) use base e (approximately 2.718). Each type of logarithm has specific applications; common logarithms are often used in scientific calculations, while natural logarithms are prevalent in calculus and continuous growth models. Knowing when to use each type is crucial for accurate calculations.

Calculator Functions

Most scientific calculators have dedicated functions for calculating logarithms, including both common and natural logarithms. Familiarity with these functions is necessary to evaluate logarithmic expressions accurately. For example, to compute log_0.1(17), one would typically convert it using the change of base formula and then use the calculator to find the values.