Question

What is the solution to 3 + 4e^x+1 = 11?

Answer 1

What is the solution to 3 + 4e^x+1 = 11?

Solution:

$3+4e^{x+1}=11$

To solve for x, Let us subtract 3 from both sides

$3+4e^{x+1}-3=11-3$

$0+4e^{x+1}=8$

$4e^{x+1}=8$

Let us divide by 4 on both sides

$\frac{4e^{x+1}}{4} =\frac{8}{4}$

$\frac{1e^{x+1}}{1} =\frac{2}{1}$

$e^{x+1} =2$

Let us take ln on both sides

$ln (e^{x+1}) =ln(2)$

So, x+1=ln(2)

To solve for x, Let us subtract 1 from both sides

x+1-1=ln(2) -1

x+0=ln(2)-1

x= ln(2) -1

Answer: Option (A)

x=ln(2)-1

Answer 2

The given equation is

$3+ 4e^{x+1} = 11$

And we have to solve for x .

First we subtract 3 to both sides, to get rid of 3 and move it to right side, that is

$4e^{x+1} = 8$

Now we need to get rid of 4, and for that , we divide both sides by 4, that is

$e^{x+1} = 2$

Now we need to get rid of e, and for that, we take natural log ln  to both sides,that is

$x+1= ln(2)$

The final step is to subtract 1, and we will get

$x = ln(2) -1$

Correct option is the first option .