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

In summary, a graph of ln(x) is a logarithmic graph that plots the natural logarithm of a number, x, on the x-axis and the value of ln(x) on the y-axis. To plot ln(x) on a graph, you can use a graphing calculator or software, or create a table of values. The domain of ln(x) is all positive real numbers greater than 0, and the range is all real numbers. The key features of the graph include a curved shape, a vertical asymptote at x=0, and an intercept at (1,0). The graph is related to the graph of e^x as their inverse functions, with points on one graph being equivalent to the points on the

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

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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).

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

1. What is a graph of ln(x)?

A graph of ln(x) is a logarithmic graph that plots the natural logarithm of a number, x, on the x-axis and the value of ln(x) on the y-axis. It is a curved line that increases slowly as x increases.

2. How do I plot ln(x) on a graph?

To plot ln(x) on a graph, you can use a graphing calculator or a graphing software. Simply input the equation ln(x) into the function or y= menu, and the graph will be generated. Alternatively, you can create a table of values by choosing specific values for x and calculating the corresponding values of ln(x), then plot those points on the graph.

3. What is the domain and range of ln(x)?

The domain of ln(x) is all positive real numbers greater than 0, since the natural logarithm function is only defined for positive numbers. The range of ln(x) is all real numbers, as the graph of ln(x) extends to negative infinity on the y-axis.

4. What are the key features of a graph of ln(x)?

The key features of a graph of ln(x) include a curved shape that increases slowly, a vertical asymptote at x=0, and an intercept at (1,0). The graph also approaches the x-axis but never touches it, and the y-values increase at a decreasing rate as x increases.

5. How is the graph of ln(x) related to the graph of e^x?

The graph of ln(x) and the graph of e^x are inverse functions of each other, meaning they are reflections of each other over the line y=x. This means that the graph of ln(x) can be obtained by reflecting the graph of e^x over the line y=x, and vice versa. Additionally, the point (x,y) on the graph of ln(x) is equivalent to the point (y,x) on the graph of e^x.