# Graph 5 log base 7 of x-2 5log7(x-2)
Find the asymptotes.
Set the argument of the logarithm equal to zero.
(x-2)5=0
Solve for x.
Set x-2 equal to 0 and solve for x.
Set the factor equal to 0.
x-2=0
Add 2 to both sides of the equation.
x=2
x=2
The solution is the result of x-2=0.
x=2
x=2
The vertical asymptote occurs at x=2.
Vertical Asymptote: x=2
Vertical Asymptote: x=2
Find the point at x=3.
Replace the variable x with 3 in the expression.
f(3)=5log7((3)-2)
Simplify the result.
Subtract 2 from 3.
f(3)=5log7(1)
Logarithm base 7 of 1 is 0.
f(3)=5⋅0
Multiply 5 by 0.
f(3)=0
0
0
Convert 0 to decimal.
y=0
y=0
Find the point at x=9.
Replace the variable x with 9 in the expression.
f(9)=5log7((9)-2)
Simplify the result.
Subtract 2 from 9.
f(9)=5log7(7)
Logarithm base 7 of 7 is 1.
f(9)=5⋅1
Multiply 5 by 1.
f(9)=5
5
5
Convert 5 to decimal.
y=5
y=5
Find the point at x=4.
Replace the variable x with 4 in the expression.
f(4)=5log7((4)-2)
Simplify the result.
Subtract 2 from 4.
f(4)=5log7(2)
5log7(2)
5log7(2)
Convert 5log7(2) to decimal.
y=1.78103593
y=1.78103593
The log function can be graphed using the vertical asymptote at x=2 and the points (3,0),(9,5),(4,1.78103593).
Vertical Asymptote: x=2
xy3041.78195
Graph 5 log base 7 of x-2     