Option A: 4 is the solution
Explanation:
The given expression is ![\log (t-3)=\log (17-4 t)](https://tex.z-dn.net/?f=%5Clog%20%28t-3%29%3D%5Clog%20%2817-4%20t%29)
We need to determine the solution of the expression.
<u>Solution:</u>
The solution of the expression can be determined by solving the expression for t.
Let us solve the given expression.
Applying the log rule, if
then ![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
Thus, we have;
![t-3=17-4 t](https://tex.z-dn.net/?f=t-3%3D17-4%20t)
Adding both sides of the equation by 4t, we get;
![5t-3=17](https://tex.z-dn.net/?f=5t-3%3D17)
Adding both sides of the equation by 3, we have;
![5t=20](https://tex.z-dn.net/?f=5t%3D20)
Dividing both sides of the equation by 5, we get;
![t=4](https://tex.z-dn.net/?f=t%3D4)
Hence, the value of t is 4.
Therefore, the solution of the given expression is 4.
Thus, Option A is the correct answer.