What is a Logarithm?

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What exactly [i]is[/i] a [b][color=#9900ff]logarithm[/color][/b]? How does/do your observation(s) support your response? Explain.
Move the LARGE POINT on the xAxis as far as it will go. You can drag the LARGE POINT that appears behind it anywhere you'd like.
What exactly [i]is[/i] a [color=#9900ff][b]natural logarithm[/b][/color]? How does/do your observation(s) support your response? Explain.
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– Tim Brzezinski

Information: What is a Logarithm?