Question

How do you graph $$\ln x$$?

Answer 1

Hint: The logarithm base b of a number n is the number x that when b is raised to $$x^{th}$$ power, the resulting value is n. That is, this can be written as $${\log }_{b}n=x\Rightarrow b^x=n$$. The logarithm with base $$e$$ is called the natural logarithm representing the $$\ln$$ function. So, we can write the logarithm base $$e$$ of a number n is the number x which can be expressed in exponents as $$\ln n={\log }_{e}n=x\Rightarrow e^x=n$$.


Complete step by step answer:
$$\ln$$ is called the natural logarithm with base $$e$$ and $$\ln x$$is also called an inverse of exponential function$$e^x$$. $$e$$ is an irrational number which is a constant and its value is 2.718281828459. It can also be written as $${\log }_{e}x$$. $$\ln x$$is undefined when $$x\underset{―}{<}0$$.
If we observe the given expression, we get to know that the base of this logarithmic function is $$e$$ which is a natural logarithm.
We can directly find the logarithmic graph by taking the image of a graph of an exponential function with respect to any of the lines$$y=\pm x$$ based on the existence of the graphs.
The below graph says that $$\ln x$$ is the image of $$e^x$$ through $$y=x$$.
In the below graph, first we draw a graph of $$e^x$$and $$y=x$$ then we take the image of $$e^x$$ which is the graph of $$\ln x$$. In this way we draw the graph of $$\ln x$$.

The graph of $$y=\ln x$$ is shown in the below figure:

Note:
We should be thorough with the logarithm and exponent concept to avoid mistakes like taking base 10 for $$\ln$$ function instead of $$e$$. $$\ln x$$ is valid only for values $$x>0$$. $$\ln x$$ meets $$x-axis$$only at $$(1,0)$$. $$e^x$$gives only positive values.