Use a calculator to find an approximation to four decimal places for each logarithm. log₂/₃ 5/8

Key Concepts

Logarithms

A logarithm is the power to which a base must be raised to produce a given number. In the expression log_b(a), b is the base, and a is the number. Understanding logarithms is essential for solving equations involving exponential growth or decay, as well as for converting multiplicative relationships into additive ones.

Change of Base Formula

The change of base formula allows you to convert logarithms from one base to another, which is particularly useful when using calculators that typically only compute logarithms in base 10 or base e. The formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number. This enables the calculation of logarithms with bases that are not directly supported by the calculator.

Approximation and Rounding

Approximation involves estimating a value that is close to the exact answer, often used in calculations where precision is not critical. Rounding is the process of reducing the number of significant digits in a number. In this context, finding an approximation to four decimal places means calculating the logarithm and then rounding the result to four digits after the decimal point for clarity and simplicity.