Question

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

Answer 1

Answer: 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:

$x=1.252$