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

Answer and Explanation :

To find : How will the graph of compare to the graph of ?

Solution :

We know that,

means the base 10 logarithm.

means the base e logarithm.

The graph of and touches at point (1,0).

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

The graph of 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.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

21

step-by-step explanation: