5log7(x-2)

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

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

The final answer is 0.

0

0

Convert 0 to decimal.

y=0

y=0

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

The final answer is 5.

5

5

Convert 5 to decimal.

y=5

y=5

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)

The final answer is 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