Question

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

Answer 1

Answer and Explanation :

To find : How will the graph of $\log x$ compare to the graph of $\ln x$?

Solution :

We know that,

$\log x$ means the base 10 logarithm.

$\ln x$ means the base e logarithm.

The graph of $\log x$ and $\ln x$ touches at point (1,0).

The graph of $\log x$ is stretched more as x increases, the y values continue to increase.

The graph of $\ln x$ increases at a faster rate as x increases.

The major difference between them is to be that the y-values in the natural log graph increase at a faster rate than the y-values for the common logarithm graph.

Refer the attached figure below.

Answer 2

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.