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A logarithmic function is not the same as an exponential function, but they are closely related. Logarithmic functions are the inverses of their respective exponential functions.

For the function y=ln(x), its inverse is x=ey

For the function y=log3(x), its inverse is x=3y

For the function y=4x, its inverse is x=log4(y)

For the function y=ln(x-2), its inverse is x=ey+2

By using the properties of logarithms, especially the fact that a number raised to a logarithm of base itself equals the argument of the logarithm:

aloga(b)=b

you can see that an exponential function with x as the independent variable of the form y=f(x) can be transformed into a function with y as the independent variable, x=f(y), by making it a logarithmic function. For a generalization:

y=ax transforms to x=loga(y) and vice-versa

Graphically, the logarithmic function is the corresponding exponential function reflected by the line y = x.

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Q: A logarithmic function is the same as an exponential function?
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Related questions

How do you change an exponential functions to a logarithmic function?

If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.


Is an exponential function is the inverse of a logarithmic function?

No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.


Is the inverse of an exponential function the quadratic function?

No. The inverse of an exponential function is a logarithmic function.


What is the difference between a logarithmic function and a natural exponential function?

The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.


A logarithmic function takes the exponential function's and returns the exponential function's input?

output


A logarithmic function takes the exponential function's output and returns the exponential function's?

input


What is the relationship between a logarithmic function and its corresponding graph in terms of the log n graph?

The relationship between a logarithmic function and its graph is that the graph of a logarithmic function is the inverse of an exponential function. This means that the logarithmic function "undoes" the exponential function, and the graph of the logarithmic function reflects this inverse relationship.


A logarithmic function is the inverse of an exponential function?

Yes.


What do you call the inverse function of the exponential function?

Logarithmic Function


An exponential function is the inverse of a logarithmic function?

Yes, y = loga(x) means the same as x=ay.


What is the purpose of semi logarithm?

The y-axis on a semi logarithmic chart is exponential. This way, when an exponential function is depicted in the chart, it will evolve as a linear function. You often do this to proove that the function is exponential and/or as a tool to help you find the equation for the function. For more see: http://www.answers.com/topic/semi-logarithmic-plot


What is the inverse of y equals log3x?

Since the logarithmic function is the inverse of the exponential function, then we can say that f(x) = 103x and g(x) = log 3x or f-1(x) = log 3x. As we say that the logarithmic function is the reflection of the graph of the exponential function about the line y = x, we can also say that the exponential function is the reflection of the graph of the logarithmic function about the line y = x. The equations y = log(3x) or y = log10(3x) and 10y = 3x are different ways of expressing the same thing. The first equation is in the logarithmic form and the second equivalent equation is in exponential form. Notice that a logarithm, y, is an exponent. So that the question becomes, "changing from logarithmic to exponential form": y = log(3x) means 10y = 3x, where x = (10y)/3.