Write the equation in exponential form. Assume that all constants are positive and not equal to 1.
[tex]log _b(p)=m[/tex]
Answer (1)
The problem requires converting a logarithmic equation to its exponential form. By applying the definition of logarithm, the equation lo g b ( p ) = m is transformed into its equivalent exponential form b m = p . The final answer is b m = p .
Explanation
Understanding the Problem The problem gives us a logarithmic equation lo g b ( p ) = m and asks us to convert it into its equivalent exponential form. We know that the logarithm is the inverse operation to exponentiation.
Applying the Definition of Logarithm The definition of a logarithm states that if lo g b ( p ) = m , then b m = p . In other words, the base b raised to the power of m equals p .
Converting to Exponential Form Therefore, the exponential form of the given equation lo g b ( p ) = m is b m = p .
Final Answer So, the equation lo g b ( p ) = m in exponential form is b m = p .
Examples
Logarithmic scales are used to represent large ranges of values in a more manageable way. For example, the Richter scale, used to measure the magnitude of earthquakes, is a logarithmic scale. An increase of 1 on the Richter scale corresponds to a tenfold increase in the amplitude of the earthquake waves. Similarly, the pH scale, used to measure the acidity or alkalinity of a solution, is also a logarithmic scale. These scales make it easier to compare vastly different values and understand their relative differences.
