FIND VERTICAL ASYMPTOTE OF LOG FUNCTION
Let
f(x) = a logn(x + c) + d (or) f(x) = a log(x + c) + d
To find the vertical asymptote of a logarithmic function, set bx + x equal to zero and solve. This will yield the equation of a vertical line. In this case, the vertical line is the vertical asymptote.
Example :
Find the vertical asymptote of the function
f(x) = log3(4x - 3) - 2
Solution :
4x - 3 = 0
4x = 3
x = 3/4
So, the vertical asymptote of the function is 3/4.
Find the vertical asymptote of each of the following logarithmic functions.
Problem 1:
f(x) = log5 x + 2
Solution :
f(x) = log5 x + 2
x = 0
Problem 2 :
f(x) = log3 (4x - 1) - 2
Solution :
f(x) = log3 (4x - 1) - 2
4x - 1 = 0
4x = 1
x = 1/4
Problem 3 :
f(x) = -log2 3x
Solution :
f(x) = -log2 3x
-3x = 0
-x = 0
x = 0
Problem 4 :
f(x) = log2 (5 - x)
Solution :
f(x) = log2 (5 - x)
5 - x = 0
-x = -5
x = 5
Problem 5 :
f(x) = log5 (-x) + 5
Solution :
f(x) = log5 (-x) + 5
-x = 0
x = 0
Problem 6 :
f(x) = ln x - 4
Solution :
f(x) = ln x - 4
x = 0
Problem 7 :
f(x) = ln (2 - 3x)
Solution :
f(x) = ln (2 - 3x)
2 - 3x = 0
-3x = -2
x = 2/3
Problem 8 :
f(x) = log3 (x + 5) + 1
Solution :
f(x) = log3 (x + 5) + 1
x + 5 = 0
x = -5
Problem 9 :
f(x) = ln (x - 3)
Solution :
f(x) = ln (x - 3)
x - 3 = 0
x = 3
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