Logarithm of the degree (coefficient before the logarithm)

Logarithmic degrees is calculated by multiplying the exponent of the sublogarithmic expression by the same logarithm, but without the degree.

logb (x y) = y ⋅ logb x

This property must meet the following conditions:

  • b>0 and b≠1;
  • x y>0.

The above formula can be considered in the opposite direction, namely:

Coefficient before logarithm can be introduced into the sublogarithmic expression in the form of its degree.

y ⋅ logb x = logb (x y)

As for any logarithm, here: b>0 and b≠1, x> 0

examples:

  • log4 63 = 3 ⋅ log4 6
  • log12 57 = 7 ⋅ log12 5
  • 4 ⋅ log7 9 = log7 94

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