Answer:
The correct answer should be:
[tex]y=\frac{1}{2}(e^3+1)\text{ or } y=\frac{e^3}{2}+\frac{1}{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]\ln(2y-1)=3[/tex]
Let’s remove the natural logarithm by raising both sides to e. This yields:
[tex]e^{\ln(2y-1)}=e^3[/tex]
The left will simplify to:
[tex]2y-1=e^3[/tex]
Add 1 to both sides:
[tex]2y=e^3+1[/tex]
Divide both sides by 2. So, the value of y should be:
[tex]y=\frac{1}{2}(e^3+1)[/tex]
