Identify the x-intercept of the function f(x) = 2 ln(x-3).
a. x=3
b. x=0
c. x=2
d. x=4
e. The function has no x-intercept
recall that ln 1 = 0
so x-3 = 1
x = 4
To identify the x-intercept of the function f(x) = 2 ln(x-3), we need to find the value of x when f(x) is equal to zero.
Setting f(x) equal to zero, we have:
2 ln(x-3) = 0
Now, since ln(x-3) = 0, we can solve for x:
ln(x-3) = 0
e^0 = x-3
1 = x-3
x = 1 + 3
x = 4
Therefore, the x-intercept of the function f(x) = 2 ln(x-3) is x = 4.
So, the correct answer is d. x=4.
To identify the x-intercept of the function f(x) = 2 ln(x-3), we need to find the value(s) of x for which the function crosses or intersects the x-axis. This occurs when f(x) is equal to zero.
Let's set f(x) = 0 and solve for x:
0 = 2 ln(x-3)
To eliminate the natural logarithm, we can rewrite the equation in exponential form:
e^0 = e^(2 ln(x-3))
Since e^0 = 1 and e^(2 ln(x-3)) is the same as (e^ln(x-3))^2 = (x-3)^2, we have:
1 = (x-3)^2
Taking the square root of both sides:
√1 = √(x-3)^2
1 = x - 3
Now adding 3 to both sides:
1 + 3 = x - 3 + 3
4 = x
Therefore, the x-intercept of the function is x = 4.
The correct answer is d. x=4.