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logs and exponential functions being inverses of each other so when you graph the inverse of a function graphically what it is its the reflection over this line y equals x this 45 degree line so if we reflect this graph all over the line y equals x what we get is the logarithm graph ok the logarithmic graph and what you can see here is that with the exponential graph it gets closer and closer to the x-axis this is an asymptote ok a horizontal asymptote the log graph though gets closer and closer to the vertical asymptote the y axis okay so the domain is X is greater than zero see this graph here its greater than zero and it goes down to negative infinity it keeps going up to positive infinity so the range will be all real numbers okay this graph goes up faster faster the log graph goes up slower and slower but it does keep going up to the right there okay so lets look at some specific examples now lets say we want to graph y equals log base two of X minus 1 plus 3 ok what does the