What is the value of x in the equation below?

1+2e^x+1=9

Answers

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

x=1.2528

Step-by-step explanation:

Assuming the equation to solve is

1+2e^x+1=9

We can first simplify as:

1+2e^x+1=9\\2+2e^x=9\\2e^x=9-2\\2e^x=7\\e^x=\frac{7}{2}

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:

ln(a^x)=xln(a)

And also remember that ln e = 1

Now we have:

e^x=\frac{7}{2}\\ln(e^x)=ln(\frac{7}{2})\\xln(e)=ln(\frac{7}{2})\\x(1)=ln(\frac{7}{2})\\x=ln(\frac{7}{2})\\x=1.2528

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

 x1.252

Step-by-step explanation:

Given the equation 1+2e^x+1=9, add the like terms:

2e^x+2=9

Subtract 2 from both sides:

2e^x+2-2=9-2

2e^x=7

Divide both sides by 2:

\frac{2e^x}{2}=\frac{7}{2}\\\\e^x=\frac{7}{2}

Apply natural logarithm to both sides. Remember that

ln(e)=1 and  ln(m)^n=nln(m)

Then, you get:

ln(e)^x=ln(\frac{7}{2})\\\\xln(e)=ln(\frac{7}{2})\\\\x=ln(\frac{7}{2})

x1.252

1.252

Explanation:

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

1+2e^x+1=9   (1)

Firstly, we have to clear x:

2e^x=9-1-1  

2e^x=7  

e^x=\frac{7}{2}     (2)

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

ln(e^x)=ln(\frac{7}{2})     (3)

xln(e)=ln(\frac{7}{2})     (4)

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

x=ln(\frac{7}{2})     (5)

Finally:

x=1.252    

X = In4-1    C on edge, just took the test

I am sure the correct answer is x=0.38629436…hope this help you


Do you know the answer?

Other questions on the subject: Mathematics

solution: →c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.that is, number of columns of a= number of rows of b.so, size of m...Read More
1 more answers
Mathematics, 21.06.2019, kevon9008
step-by-step explanation: i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i...Read More
1 more answers