Express as a product. [tex]$\log M^{20}$[/tex]
Answer (1)
Apply the power rule of logarithms, which states that lo g b ( x p ) = p lo g b ( x ) .
Apply the power rule to the given expression: lo g M 20 = 20 lo g M .
The expression lo g M 20 expressed as a product is 20 lo g M .
Explanation
Understanding the Problem We are asked to express lo g M 20 as a product. We will use the power rule of logarithms to achieve this.
Recalling the Power Rule The power rule of logarithms states that lo g b ( x p ) = p lo g b ( x ) , where b is the base of the logarithm, x is the argument, and p is the exponent.
Applying the Power Rule Applying the power rule to the given expression, we have: lo g M 20 = 20 lo g M
Examples
Logarithms are used in many scientific fields, such as physics, chemistry, and engineering. For example, the Richter scale, which measures the magnitude of earthquakes, is a logarithmic scale. The formula you used here is essential for simplifying logarithmic expressions, which can be useful in calculations involving exponential growth or decay, such as population growth or radioactive decay. Understanding how to manipulate logarithms allows scientists and engineers to solve complex problems more easily.
