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The tutorial discusses graphing logarithmic functions by explaining the four basic shapes. If both x and y are positive, the graph moves towards quadrant one. Logarithmic functions are the inverse of exponential functions and have a vertical asymptote. Exponential functions increase at an increasing rate, while logarithmic functions increase at a decreasing rate. When plotting 2 to the x and log base 2 of x on the same graph, they form inverse functions that reflect across the line y equals x. The graph of log of negative x is not explicitly mentioned in the provided text.