Exponential form is ax = b.
Logarithmic form is logab = x.
For example, 102 = 100 is the same as log10100 = 2.
Another example: 53 = 125 is the same as log5125 = 3.
If there is no number under the log (for example, log3), the the number is understood to be ten. For example, log8 is the same as log108.
A natural log uses the symbol ln. In this case, the number is understood to be e (which equals about 2.718). For example, ln5 is the same as loge5 (which the same as log2.7185).
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Exponential growth
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Logarithmic equation
Logarithmic functions are converted to become exponential functions because both are inverses of one another.
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.