Logarithmic Functions

What are Logarithmic Functions?

The reverse of exponentiation function is referred to as logarithmic function.

What is the Basic Logarithmic Function Example?

The basic logarithmic function example includes y = log₃ x.

What is Natural Logarithmic Function?

The logarithmic function with base e is called natural logarithmic function.

What are common bases used in logarithmic functions?

The most common bases used in logarithmic functions are:

• Base 10 (common logarithm): log⁡₁₀(x), often written as log⁡(x)
• Base e (natural logarithm): log⁡_e(x), often written as ln⁡(x).
• Base 2: log_⁡2(x)

What are the properties of logarithms?

Some important properties of logarithms include:

• Product Rule: log_⁡b(xy) = log_⁡b(x) + log⁡_b(y)
• Quotient Rule: log⁡_b(x/y)=log_⁡b(x) − log⁡_b(y)
• Power Rule: log⁡_b(x^k)=klog⁡_b(x)
• Change of Base Formula: log_⁡b(x)=log⁡_k(x)\log⁡_k(b)​, where k is any positive number

What is the domain and range of a logarithmic function?

• The domain of a logarithmic function y = log⁡_b(x) is x>0.
• The range of a logarithmic function y = log⁡_b(x) is all real numbers (−∞ < y < ∞)

Logarithmic functions are the reverse function of exponentiation. The basic logarithmic function is log_ex where e is the base of the logarithmic function. In this article, we will see the important formulas of logarithmic functions and solve some examples related to the logarithmic functions.