Answer:
The value of x = -0.17
Step-by-step explanation:
∵ [tex]2e^{8x}=1-e^{4x}[/tex]
Let [tex]e^{4x}=y[/tex]
∴ [tex]e^{8x}=y^{2}[/tex]
∴ 2y² = 1 - y
∴ 2y² + y - 1 =0 ⇒ factorize
∴ (2y - 1)(y + 1) = 0
∴ 2y - 1 = 0 ⇒ 2y = 1 ⇒ y = 1/2
∴ y + 1 = 0 ⇒ y = -1
∵ [tex]y=e^{4x}[/tex]
Note: [tex]e^{4x}=-1[/tex] ⇒ refused
([tex]e^{ax}[/tex] never gives -ve values)
∴ [tex]e^{4x}= 1/2[/tex] ⇒ insert ln in both sides
∵ [tex]ln(e)^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1
∴ 4xln(e) = ln(1/2) ⇒ 4x = ln(1/2)
∴ x = [ln(1/2)]/4 = -0.17
