Question

What is the value of x in the equation below 1+2e^x+1=9

Answer 1

`x=1.2528`

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=(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=(7)/(2)\\ln(e^x)=ln((7)/(2))\\xln(e)=ln((7)/(2))\\x(1)=ln((7)/(2))\\x=ln((7)/(2))\\x=1.2528`

Answer 2

Answer:
`x`≈
`1.252`

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:

`(2e^x)/(2)=(7)/(2)\\\\e^x=(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((7)/(2))\\\\xln(e)=ln((7)/(2))\\\\x=ln((7)/(2))`

`x`≈
`1.252`