lim as x approaches positive 3 ln(x-3)
Knowing what the basic log function looks like,
lim ln(x-3) as x approaches positive 3 is negative infinity
www.wolframalpha.com/input/?i=plot+y+%3D+log(x-3)+from+0+to+10
To find the limit as x approaches positive 3 of ln(x-3), we can use the properties of logarithms and the concept of limits.
First, let's rewrite the limit expression as x approaches 3 of ln(x-3).
The natural logarithm ln(x) is defined for positive values of x. On the other hand, the expression ln(x-3) is defined for x-3 > 0, which means x > 3.
Since we are interested in the limit as x approaches 3 from the positive side, we need to consider the values of x that are slightly greater than 3.
As x approaches 3 from the positive side, the value of (x-3) approaches 0. When the argument of the natural logarithm approaches 0, the value of ln(x-3) tends to negative infinity.
So, the limit as x approaches 3 from the positive side of ln(x-3) is negative infinity, denoted as lim x→3+ ln(x-3) = -∞.
In summary, the limit as x approaches positive 3 of ln(x-3) is negative infinity.