log(m×n×p) ≟ log(m) + log(n) + log(p)



Let log(m) = A,  then by the definition of logarithms, m = 10A.

Let log(n) = B,  then by the definition of logarithms, n = 10B.

Let log(p) = C,  then by the definition of logarithms, p = 10C.

Then m×n×p = 10A×10B×10C = 10A+B+C 

Since m×n×p = 10A+B+C

then by definition of logarithms,

log(m×n×p) = A+B+C.  Substituting for A, B and C,

log(m×n×p) = log(m) + log(n) + log(p) 

That's what we had to prove.

Edwin