How will the graph of log x compare to the graph of ln x?

Both graphs pass through (1,0). Both graphs have an asymptote which is the y axis and the graph drops towards -∞ as x goes from 1 to zero. The graph of log x is shallower (assuming base 10) than ln x. For example log 10 = 1 but ln 10 is about 2.3. This value is constant when comparing the y values for the two functions. Log 100 = 2 but ln 100 = 4.6 which is 2.3 times 2. As x increases the graphs of both functions have a shallower gradient.