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# A logarithmic function is the same as an exponential function?

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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. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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