Exploring the Logarithm Function: Properties, Graph, and Representation of f(x) = logx

f(x) = logx

Let’s break down the function f(x) = logx

Let’s break down the function f(x) = logx.

The function f(x) = logx represents the logarithm of x with base 10. The logarithm function is the inverse of exponential function with base 10. It answers the question of “what power of 10 gives us x?”. In other words, if 10 raised to the power of something equals x, then that “something” is the logarithm of x with base 10.

Important Properties of the Logarithm Function:
1. Domain: The domain of the logarithm function f(x) = logx is all positive real numbers.
2. Range: The range of the logarithm function f(x) = logx is all real numbers.
3. Vertical Asymptote: The graph of the logarithm function has a vertical asymptote at x = 0. This means that the function is not defined for x ≤ 0.
4. x-Intercept: The x-intercept of the graph of the logarithm function f(x) = logx is at x = 1 since log₁₀(1) = 0.
5. Increasing or Decreasing: The logarithm function is strictly increasing. As x increases, the value of logx also increases.
6. Symmetry: The logarithm function is not symmetric about the x-axis or y-axis.

Graph of f(x) = logx:
The graph of f(x) = logx starts at (-∞, -∞) and approaches the x-axis as x approaches 0 from the right. As x increases, the value of logx also increases indefinitely. The graph never intersects the x-axis and approaches the y-axis as x approaches ∞.

Graphical representation of f(x) = logx:
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