1+2e^x+1=9

remember

ln(a^b)=bln(a)

ln(e)=1

so

ln(e^x)=xln(e)=x

1+2e^{x+1}=9

minus \space\ 1 \space\ both \space\ sides

2e^{x+1}=8

divide \space\ both \space\ sides \space\ by \space\ 2

e^{x+1}=4

take \space\ ln \space\ of \space\ both \space\ sides

ln(e^{x+1})=ln(4)

(x+1)ln(e)=ln(4)

x+1=ln(4)

minus \space\ 1 \space\ from \space\ both \space\ sides

x=ln(4)-1

answer \space\ is \space\ C=ln(4)-1

Step-by-step explanation:

Assuming the equation to solve is

We can first simplify as:

to solve an equation with e and x as an exponent, we need to take "natural log (ln)" on both sides and also use the property:

And also remember that ln e = 1

Now we have:

C

Step-by-step explanation:

1+2e^x+1=9

2e^x+1=9-1

e^x+1= 8/2

e^x+1 = 4

Here we can applicate the Ln:

ln e^x+1 = ln 4

Applicating the log property for exponent:

(x+1).ln e = ln 4

Ln e = 1, so:

x+1 = ln 4

x = ln 4-1

≈

Step-by-step explanation:

Given the equation , add the like terms:

Subtract 2 from both sides:

Divide both sides by 2:

Apply natural logarithm to both sides. Remember that

and

Then, you get:

≈

1.252

Explanation:

We are given this equation and we need to find the value of :

(1)

Firstly, we have to clear :

(2)

Applying Natural Logarithm on both sides of the equation (2):

(3)

(4)

According to the Natural Logarithm rules , so (4) can be written as:

(5)

Finally:

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