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

Answer:

Option B is correct

Step-by-step 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;

$\frac{5e^{x-2}}{5} = \frac{11}{5}$

Simplify:

$e^{x-2} = \frac{11}{5}$

Taking log both sides we get;

$lne^{x-2} = ln\frac{11}{5}$

$x-2 = \ln\frac{11}{5}$                    Using :$\ln e^x=x$

Add 2 to both sides of an equation:

$x=\ln\frac{11}{5}+2$

Therefore, the solution to $4+5e^{x-2} = 11$ is, $x=\ln\frac{11}{5}+2$