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The video tutorial discusses graphing logarithmic functions, focusing on four basic shapes. When dealing with log x where x and y are both positive, the graph travels towards quadrant one. Logarithmic functions are the inverse of exponential functions, and they contain a vertical asymptote. Exponential functions increase at an increasing rate, while logarithmic functions increase at a decreasing rate. When comparing 2^x and log base 2 of x, the graphs are inverse functions reflected across the line y = x. Reflecting about the line y = 0, the graph of log of negative x is discussed.
