Logarithms
The rule log(X⋅Y) = log(X) + log(Y) follows from the familiar law of exponents:
10
A+B
= 10
A
10
B
.
Here's how.
Write
X = 10
A
,
Y = 10
B
,
and
Z = 10
A+B
.
Then
log(X) = A,
log(Y) = B,
and
log(Z) = A+B
From the exponent law above, Z = X⋅Y.
Consequently,
log(X⋅Y) = log(Z) = A + B = log(X) + log(Y).
Return to
Logarithms
.