What is the graph of ln x if I know the graph of e^x?

Thread starter Drimar
Start date Feb 28, 2006
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Function Graphing

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SUMMARY

The graph of the natural logarithm function, y = ln x, can be derived from the graph of the exponential function, y = e^x, by swapping the x and y axes. This transformation highlights that if y = ln x, then x = e^y. Additionally, reflecting the graph across the line y = x provides the same result, where the point (0, 1) on the e^x graph corresponds to (1, 0) on the ln x graph.

PREREQUISITES

Understanding of exponential functions, specifically y = e^x
Knowledge of logarithmic functions, particularly y = ln x
Familiarity with graph transformations, including axis swapping
Basic concepts of reflection in geometry

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Study the properties of logarithmic functions and their graphs
Explore the relationship between exponential and logarithmic functions
Learn about graph transformations, including reflections and rotations
Investigate the applications of ln x in calculus and real-world scenarios

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Students in K-12 education, particularly those studying algebra and precalculus, as well as educators seeking to explain the relationship between exponential and logarithmic functions.

Feb 28, 2006

Drimar

I am still in k12, what is a graph of lnx if i know what e^x looks like ?

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Feb 28, 2006

HallsofIvy

Science Advisor

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If y= ln x then x= e^y. Just swap your x and y axes. Another way to do the same thing is to draw the line y= x and "reflect" the graph in that. That is, the point (0,1) becomes (1, 0).