Which multiplier gives a faster rate of increase, exponential or logarithmic?
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DaphneT (
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August 22nd, 2012
If I say something has increased exponentially, has it increased faster or slower than something that has increased logarithmically?
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8 Answers
Exponential. Try exponentially putting money on a checker board, start with square one with one a penny…
Logarithmic growth is much, much slower.
Log is like exponential growth flipped onto its side.
Ah, thanks. I had that one backwards. Must go use in a sentence, if I can remember where I wanted to use it. Thanks again.
Log 100 = 2. (assuming base 10).
10 squared = 100.
I agree with the above answers, but note that the term ‘logarithmic’ is sometimes used to mean exponential.
@gasman, :) that is precisely why I wanted to clarify which meant which. I knew that logarithmic is expansion at a different rate than exponential, just couldn’t remember the correct speed, relative to each other.
@DaphneT: they are inverse functions. If you plot the exponential function y = exp(x), then flip on its side as @Qingu said, interchanging x and y axes, then you get x = log(y).
An example of confusion in terminology is in bacterial growth. Quoting Wikipedia
Exponential phase (sometimes called the log phase or the logarithmic phase) is a period characterized by cell doubling…For this type of exponential growth, plotting the natural logarithm of cell number against time produces a straight line.
To try and put this simply, exponential growth is the straight forward one, the proportion of growth is constant, and therefore growth is ever increasing at a faster and faster rate.
logarithmic is the strange one best left for when theres some paracetamols lying about, but put simply, it is the inverse of exponential growth, and growth is at an ever decreasing rate.
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