Logarithmic Expressions, Equations, and Functions

Full Answer Section

log₂(8) = 3

Here, "log₂(8)" is read as "log base 2 of 8." It's asking, "What power of 2 gives us 8?"

Two More Examples:

1. Logarithm Base 10:

   • Exponential form: 10² = 100
   • Logarithmic form: log₁₀(100) = 2

2. Natural Logarithm (Base e):

   • Exponential form: e³ ≈ 20.086
   • Logarithmic form: ln(20.086) ≈ 3

In essence, a logarithm is the exponent that a base must be raised to in order to produce a given number. By understanding this fundamental relationship, we can solve a wide range of mathematical problems and applications.

Would you like to explore more specific applications of logarithms or delve deeper into their properties?

Sample Answer

A Logarithm is an Exponent: A Closer Look

Understanding the Basics

A logarithm is essentially the inverse operation of exponentiation. To better understand this, let's break down the concept.

When we say "2 raised to the power of 3 equals 8," we're expressing an exponential equation:

2^3 = 8

Now, let's ask the inverse question: "What power do we raise 2 to in order to get 8?" The answer, of course, is 3. This is where logarithms come into play. We can express this question and answer in logarithmic form: