How do you prove log(n + 1) = log(n) + 1 for integers n >= 1???

Answer 1

is this your homework ?

Answer 2

You don't; it is false.

For, if n = 0, then log (n + 1) = log 1 = 0, but log n + 1 = log 0 + 1, which is undefined, because no x satisfies e^x = 0.

If you don't like "undefined", then if n = 1, then log (n + 1) = log 2, which is between 0 and 1, since 2 is between 1 and 10. Meanwhile, log n + 1 = log 1 + 1 = 0 + 1 = 1, which is clearly different.

In fact, the only solution to the equation is that of log (n+1) = log n + log 10, or that of log (n+1) = log 10n; you do the rest.

Answer 3

You can't, because it doesn't. Try a quick check: log(5) = 0.69897, log(6) = 0.778151. log(6) does not equal log(5) + 1.

Answer 4

NO PROVE It´s NOT TRUE