Answer:
- [tex]\boxed{\sf{x=84}}[/tex]
Step-by-step explanation:
This problem can be solved by using the logarithm function.
Isolate the term of x from one side of the equation.
First, you divide by -6 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{-6\log _3(x-3)}{-6}=\dfrac{-24}{-6}}[/tex]
Solve.
Divide the numbers from left to right.
-24/-6=4
Rewrite the problem down.
[tex]\Longrightarrow: \sf{\log _3(x-3)=4}[/tex]
x-3=81
Add by 3 from both sides.
[tex]\Longrightarrow:\sf{x-3+3=81+3}[/tex]
Solve.
Add the numbers from left to right.
81+3=84
[tex]\Longrightarrow: \boxed{\sf{x=84}}[/tex]
- Therefore, the solution is x=84, which is our answer.
I hope this helps you! Let me know if my answer is wrong or not.
