The equation \log_b(m^k) = k \cdot \log_b(m) illustrates a property of logarithms. Here, b is the base of the logarithm, m is a positive number, and k is any real number. This property shows that the logarithm of a number raised to a power can be simplified by multiplying the exponent k by the logarithm of the base number m . This relationship is useful in various fields, including mathematics, science, and engineering, as it simplifies calculations involving exponential growth or decay. By breaking down complex logarithmic expressions, it allows for easier manipulation and understanding of relationships between numbers.