# Graph (1/7) natural log of x (17)ln(x)
Find the asymptotes.
Set the argument of the logarithm equal to zero.
x17=0
Solve for x.
Raise each side of the equation to the 7 power to eliminate the fractional exponent on the left side.
(x17)7=(0)7
Raising 0 to any positive power yields 0.
x=0
x=0
The vertical asymptote occurs at x=0.
Vertical Asymptote: x=0
Vertical Asymptote: x=0
Find the point at x=1.
Replace the variable x with 1 in the expression.
f(1)=(17)ln(1)
Simplify the result.
The natural logarithm of 1 is 0.
f(1)=17⋅0
Multiply 17 by 0.
f(1)=0
0
0
Convert 0 to decimal.
y=0
y=0
Find the point at x=2.
Replace the variable x with 2 in the expression.
f(2)=(17)ln(2)
Simplify the result.
Combine 17 and ln(2).
f(2)=ln(2)7
ln(2)7
ln(2)7
Convert ln(2)7 to decimal.
y=0.09902102
y=0.09902102
Find the point at x=3.
Replace the variable x with 3 in the expression.
f(3)=(17)ln(3)
Simplify the result.
Combine 17 and ln(3).
f(3)=ln(3)7
ln(3)7
ln(3)7
Convert ln(3)7 to decimal.
y=0.15694461
y=0.15694461
The log function can be graphed using the vertical asymptote at x=0 and the points (1,0),(2,0.09902102),(3,0.15694461).
Vertical Asymptote: x=0
xy1020.09930.157
Graph (1/7) natural log of x     