Question

Jenn claims that because log(1) + log(2) + log(3) = log(6), then log(2) + log(3) + log(4) = log(9).

Is she correct? Explain how you know.

Answer 1

No, she is not correct

Explanation:

Hi there!

In the first case it works because of this logarithm property:

log (a·b) = log a + log b

Let´s see:

log (6) = log(1) + log(2) + log(3)

because 6 = 1 · 2 · 3

So, instead log(6) we can write:

log(1 · 2 · 3)

And by the property of logarithm written above:

log(6) = log(1 · 2 · 3) = log(1) + log(2) + log(3)

In the second case:

9 ≠ 2 · 3 · 4

Then:

log(9) ≠ log(2 · 3 · 4)

Thus

log(9) ≠ log (2) + log(3) + log(4)

Have a nice day!