Question

What is the solution to 4+5e^x=2=11?

Ax= In7/5-2
Bx= In7/5+2
Cx= In35-2
D x=In35+2

Answer 1

4+5e^(x-2)=11
4+5e^(x-2)-4=11-4
5e^(x-2)=7
5e^(x-2) / 5 = 7/5
e^(x-2)=7/5
ln e^(x-2) = ln (7/5)
(x-2) ln e = ln (7/5)
(x-2) (1) = ln (7/5)
x-2=ln (7/5)
x-2+2=ln (7/5)+2
x = ln (7/5) + 2

Answer: Otion B. x= ln (7/5) +2

Answer 2

Option B is correct

Explanation:

Given the equation:
`4+5e^(x-2) = 11` ......[1]

Subtraction property of equality states that you subtract the same number to both sides of an equation.

Subtract 4 to both sides in equation [1];

`4+5e^(x-2) -4 = 11-4`

Simplify:

`5e^(x-2)= 11`

Divide both sides by 5 we get;

`(5e^(x-2))/(5) = (11)/(5)`

Simplify:

`e^(x-2) = (11)/(5)`

Taking log both sides we get;

`lne^(x-2) = ln(11)/(5)`

`x-2 = \ln(11)/(5)` Using :
`\ln e^x=x`

Add 2 to both sides of an equation:

`x=\ln(11)/(5)+2`

Therefore, the solution to
`4+5e^(x-2) = 11` is,
`x=\ln(11)/(5)+2`