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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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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.
