Question 1070568
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log(m×n×p) &#8799; log(m) + log(n) + log(p)



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

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

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

Then m×n×p = 10<sup>A</sup>×10<sup>B</sup>×10<sup>C</sup> = 10<sup>A+B+C</sup> 

Since m×n×p = 10<sup>A+B+C</sup>

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</pre></b></font>