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Exponents and logarithms are inverse operations. As functions, they are also inverses of each other. There is a special relationship between inverse functions on a graph: the line 
is a line of symmetry or reflection between a function and its inverse. So we should expect this relationship to hold true when examining the graphs of an exponential function and a logarithmic function:
As we can see in the graph above, since a function is symmetrical about the line to its inverse, we can swap x- and y-values to plot points on a function's inverse. This also means that the domain and range of a function switches as we describe the domain and range of its inverse. That is, the domain of a function becomes the range of its inverse, and the range of a function becomes the domain of its inverse.
Looking at the graph of the exponential function, we can see that the domain is all x-values from negative infinity to positive infinity. This means that the range of logarithmic functions is all y-values, from negative infinity to positive infinity.
However, when looking at the range of the general exponential function graphed above, we see that the range is from zero to positive infinity. As the x-values approach negative infinity, the y-values approach 0 but never actually touch the x-axis. Also, there are no x values that make y negative (at least when both 
and b are positive). So the range of an exponential function is y-values greater than zero, meaning the domain of the logarithmic function is restricted to x-values greater than zero through positive infinity. Inputting a negative value into the logarithmic function will yield a non-real answer.
When studying exponential functions, you may recall that the y-intercept of 
is at (0, 1) on the graph, because when x = 0, y = 1. This is because any value raised to the power of zero evaluates to 1. When comparing this to logarithmic functions, we invert x and y (maybe you are starting to see a pattern here!). So instead of talking about the y-intercept of an exponential function, we talk about the x-intercept of a logarithmic function; and instead of having coordinates of (0, 1), it has the coordinates (1, 0). This is illustrated in the graph below:
