Whenever the data covers a very large range of values a log scale if very useful. Earthquakes and hearing are common examples.
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Exponential and logarithmic functions are inverses of each other.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
Yes.
A log-log scale is a set of axes where each axis is logarithmic in scale.
Yes, y = loga(x) means the same as x=ay.