A logarithmic function is the same as an exponential function?

Answer 1

Apex: false

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.