Question

Solve the equation. Round to the nearest hundredth. Show work.

Answer 1

Answer:

x  =  0.0116096 ,  1.91705119

Step-by-step explanation:

I looked on a site to look this up.

Answer 2

Answer:

x = 0.92

Step-by-step explanation:

To solve this, we need first use the exponent rule of  $e^{bc}=(e^b)^c$  on $e^{2x}$.  We can break it down to  $e^{2x}=(e^x)^2$. We can now re-write as:

$6(e^x)^{2}-13(e^x)-5=0$

This looks like a trinomial that we can middle term factorize by letting $y=e^x$. Thus we can write and factorize and solve as shown below:

$6(e^x)^{2}-13(e^x)-5=0\\6y^2-13y-5=0\\6y^2+2y-15y-5=0\\2y(3y+1)-5(3y+1)=0\\(2y-5)(3y+1)=0$

Thus, 2y-5 = 0 OR 3y+1 = 0

Solving we have  y = 5/2 and y = -1/3

Now bringing back the original variable of letting y = e^x, we have:

1. 5/2 = e^x, and

2. -1/3 = e^x

Solving 1:

$\frac{5}{2}=e^x\\ln(\frac{5}{2})=ln(e^x)\\x=ln(\frac{5}{2})$

Solving 2:

We will have x = ln (-1/3) WHICH IS NOT POSSIBLE because ln is never negative.

So our answer is x = ln (5/2)

Rounding to nearest hundredth: x = 0.92