Question

Does anyone know the answer for the question below.

Answer 1

Answer:

B. (1, 0)

Step-by-step explanation:

Given:

The two functions are:

$f(x)=\ln(x)\\g(x)=\ln (x^2)$

In order to determine the point of intersection of the graphs of the two given functions, we need to equate the functions.

$f(x)=g(x)\\\ln x=\ln x^2$

Two log functions with same base are equal only if their terms are equal to each other. Therefore,

$x=x^2\\\textrm{Subtracting x from both sides}\\x-x=x^2-x\\x^2-x=0\\x(x-1)=0\\\therefore x=0\ or\ x-1=0\\\therefore x=0\ or\ x=1$

But a log function is not defined for $x=0$. Therefore, the value of $x$ is only equal to 1.

Now, the $y$ value can be obtained using any one of the function.

$f(1)=\ln1-0$ ( Since, log 1 = 0)

Therefore, the point of intersection of the functions $f(x)\ and\ g(x)\ is\ (1,0)$.

The correct option is B. (1, 0).