Here is a logarithmic expression: log10(100).
A. How do we say the expression in words?
B. Explain in your own words what the expression means.
C. What is the value of this expression?
The correct answer and explanation is:
A. How to say the expression in words:
The expression log10(100) is read as “logarithm base 10 of 100.”
B. What the expression means:
The logarithmic expression log10(100) is asking the question: “To what power must 10 be raised to obtain the number 100?” The base of the logarithm is 10, which is commonly referred to as the common logarithm.
In simpler terms, the logarithm tells us the exponent or power needed to raise the base (in this case, 10) to produce the number inside the parentheses (in this case, 100). The general form of a logarithmic equation is: logb(x)=ywhich is equivalent toby=x\log_b(x) = y \quad \text{which is equivalent to} \quad b^y = x
Here, b is the base (10 in this case), x is the number inside the logarithm (100 here), and y is the answer, which is the exponent or power to which the base is raised to result in x.
So, log10(100) is asking: “What power of 10 equals 100?”
C. The value of the expression:
To solve log10(100), we ask, “10 raised to what power equals 100?” The answer is 2 because: 102=10010^2 = 100
Therefore, log10(100) = 2.
Explanation:
The logarithmic expression is essentially the reverse of exponentiation. While exponentiation tells us how to get a number by raising a base to a certain power (for example, 10^2 = 100), the logarithm does the opposite. It finds out what exponent is required to reach a certain number when a specific base is used. In this case, since 10^2 equals 100, the value of log10(100) is 2. This is a fundamental concept in logarithmic and exponential functions, often used in fields like science, engineering, and computer science.