OK....not too bad
Rate of change from x = 1 to x = 10 =
[ log 10 - log 1 ] [ 1 - 0 ] 1
____________ = _________ = ____
10 - 1 9 9
Rate of change from 1 to 100
[ log 100 - log 1 ] 2 - 0 2
_______________ = _________ = _____
100 - 1 99 99
Since 1/ 9 > 2 /99.....the average rate of change [ slope ] from 1 to 10 is greater than the average rate of change from 1 to 100.....but.....the rate of change between any two points will be positive...so....the slope is always positive