Logarithms

The rule log(XY) = Y⋅log(X)follows from the familiar law of exponents:

(10A)Y = 10A⋅Y.

Here's how.

Write X = 10A and Z = 10A⋅Y.

Then log(X) = A and log(Z) = A⋅Y.

From the exponent law above, Z = XY.

Consequently,

log(XY) = log(Z) = A⋅Y = Y⋅A = Y⋅log(X).

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