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It is the logarithmic function.
The y-axis on a semi logarithmic chart is exponential. This way, when an exponential function is depicted in the chart, it will evolve as a linear function. You often do this to proove that the function is exponential and/or as a tool to help you find the equation for the function. For more see: http://www.answers.com/topic/semi-logarithmic-plot
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As far as this browser allows, the answer is NO.
Natural logarithms use base e (approximately 2.71828), common logarithms use base 10.