In the context of logarithms, which of the following statements is true?
Practice Questions
1 question
Q1
In the context of logarithms, which of the following statements is true?
Logarithm of a product is the sum of the logarithms.
Logarithm of a quotient is the product of the logarithms.
Logarithm of a power is the power of the logarithm.
Logarithm of a number is always positive.
The logarithm of a product is indeed the sum of the logarithms, as per the property log(a*b) = log(a) + log(b).
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of logarithms, which of the following statements is true?
Solution: The logarithm of a product is indeed the sum of the logarithms, as per the property log(a*b) = log(a) + log(b).
Steps: 6
Step 1: Understand what a logarithm is. A logarithm answers the question: 'To what power must a certain number (the base) be raised to get another number?'
Step 2: Identify the property of logarithms we are discussing. The property states that the logarithm of a product (two numbers multiplied together) can be expressed as the sum of their individual logarithms.
Step 3: Write down the property: log(a * b) = log(a) + log(b). This means if you take the logarithm of a product (a times b), it equals the logarithm of a plus the logarithm of b.
Step 4: Verify the property with an example. For example, if a = 2 and b = 3, then log(2 * 3) = log(6) should equal log(2) + log(3).
Step 5: Calculate log(2) and log(3) using a calculator or logarithm table, then add them together to see if it equals log(6).
Step 6: Conclude that the statement about the logarithm of a product being the sum of the logarithms is true.
