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.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.