Problem 5
Question
Match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\ln u^{n}=n \ln u$$
Step-by-Step Solution
Verified Answer
The given logarithm \(\ln u^{n}=n \ln u\) corresponds to (a) Power Property.
1Step 1: Identify the given equation
The equation given in the problem is \(\ln u^{n}=n \ln u\) which implies that the power of u (n) has been transferred from being a power and now it is multiplying with the logarithm of u. Take a moment to understand the transformation.
2Step 2: Understand the logarithm properties
Review the three properties of logarithms mentioned: Power Property, Quotient Property, and Product Property. The Power Property states that the logarithm of a number raised to a power is equal to the product of the power and the logarithm of the number. The Quotient Property states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. The Product Property states that the logarithm of a product is equal to the sum of the logarithms of the factors.
3Step 3: Match the given equation with a property
Compare the given equation \(\ln u^{n}=n \ln u\) with the Power Property definition. The structure of the equation matches exactly the definition of the Power Property, hence it corresponds to the Power Property.
Other exercises in this chapter
Problem 5
A logistic growth model has the form ________.
View solution Problem 5
Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(4^{2 x-7}=64\) (a) \(x=5\) (b) \(x=2\)
View solution Problem 5
The Inverse Properties of logarithms and exponentials state that \(\log _{a} a^{x}=x\) and _____.
View solution Problem 6
A logistic curve is also called a ________ curve.
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