Question

Need help knowing if I was right with .88 and 1

Answer 1

Given

`8e^(4x)-15e^(2x)+7=0`

Then solve for x:

Apply the law of exponents

`8\left(e^x\right)^4-15\left(e^x\right)^2+7=0`

Rewrite the equation with e^x = u:

`8\left(u\right)^4-15\left(u\right)^2+7=0`

And solve for u:

`u=1,\:u=(√(14))/(4)`

Then, substitute e^x = u:

`\begin{gathered} e^x=1 \\ ln(e^x)=ln(1) \\ x=0 \end{gathered}`

and

`\begin{gathered} e^x=(√(14))/(4) \\ ln(e^x)=ln((√(14))/(4)) \\ x=ln(√(14))-ln(4) \\ x=(1)/(2)ln(14)-2ln(2) \\ x=-0.067 \end{gathered}`

Answer: x = 0 and x = - 0.067