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The video tutorial discusses graphing logarithmic functions, outlining the four basic shapes. When graphing log x where x and y are positive, the graph travels towards quadrant one. Logarithmic functions are inverses of exponential functions and contain vertical asymptotes. Exponential functions have a horizontal asymptote and increase at an increasing rate, while logarithmic functions increase at a decreasing rate. When comparing 2^x and log base 2 x on the same graph, they are inverse functions reflecting across the line y=x. The graph of log of negative x is not explicitly addressed in the text.
