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

Question

asked Nov 16, 2023 8.2k views

1 Answer

Zanetu · Answer 1 · 2023-11-22T21:20:20+0000

Given

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