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Algebra >> Exponential and Logarithmic Functions >> Graphs of Exponential and Logarithmic Functions

Math Example: Graphs of Logarithmic Functions: Example 17

Math Example: Graphs of Logarithmic Functions: Example 17

Graph of y = ln(10x)

Topic

Logarithmic Functions

Description

This example illustrates the graph of the natural logarithmic function y = ln(10x). The graph opens upward, curving from left to right, demonstrating how multiplication inside the logarithm affects the function's behavior. The domain of this function is x > 0, as the expression inside the natural logarithm must be positive.

Natural logarithmic functions with various transformations are crucial in many scientific and mathematical applications, particularly in calculus and differential equations. They are often used to model exponential growth and decay in fields such as biology, physics, and economics. This collection of examples helps teach logarithmic functions by presenting a range of equations with different parameters, allowing students to visualize and understand how these changes impact the graph's shape and position.

Exploring multiple worked-out examples is vital for students to develop a comprehensive understanding of logarithmic functions and their transformations. Each example builds upon previous knowledge, introducing new concepts and variations. This approach helps students recognize patterns, make connections between different forms of logarithmic equations, and develop problem-solving skills that can be applied to more complex scenarios involving exponential and logarithmic relationships.

Teacher's Script: Let's examine our seventeenth example, y = ln(10x). How does this graph compare to the basic natural logarithm function we saw earlier? Notice the similar shape, but can you spot any differences in its position? The domain is still x > 0, but why? Consider how the multiplication by 10 inside the logarithm affects where the graph intersects the y-axis. Can you predict this point of intersection? Remember, ln(10) is a key value in logarithmic functions.

For a complete collection of math examples related to Logarithmic Functions click on this link: Math Examples: Graphs of Logarithmic Functions Collection.

Common Core Standards CCSS.MATH.CONTENT.HSF.IF.C.7, CCSS.MATH.CONTENT.HSF.IF.C.8.B, CCSS.MATH.CONTENT.HSF.BF.B.5, CCSS.MATH.CONTENT.HSF.IF.C.7.E, CCSS.Math.CONTENT.HSF.LE.A.2, CCSS.MATH.CONTENT.HSF.LE.A.3, CCSS.MATH.CONTENT.HSF.LE.A.4, CCSS.MATH.CONTENT.HSF.LE.B.5
Grade Range 9 - 12
Curriculum Nodes Algebra
    • Exponential and Logarithmic Functions
        • Graphs of Exponential and Logarithmic Functions
Copyright Year 2013
Keywords logarithmic functions, graphs