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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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โˆ™ 2015-08-10 00:48:59
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Xavier Arndt

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โˆ™ 2021-12-04 00:50:18
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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 the inverse of an exponential function the quadratic function?

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


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.


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


A logarithmic function is the inverse of an exponential function?

Yes.


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

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.


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


Which graph best represents a logarithmic function?

an exponential function flipped over the line y=x


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.

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