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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.
What else can I help you with?
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
What do you call the inverse function of the exponential function?
Logarithmic Function
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.
Which graph best represents a logarithmic function?
an exponential function flipped over the line y=x
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
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.
A logarithmic function takes the exponential function's output and returns the exponential function's?
input
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
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.
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.
