Solve the equation. Round to the nearest hundredth. Show work.[tex]6e^{2x} - 5e^{x} = 6[/tex]

Answer:The value of x = 0.41Step-by-step explanation:∵ [tex]6e^{2x}-5e^{x}=6[/tex]Let [tex]e^{x}=y[/tex]∴ [tex]e^{2x}=y^{2}[/tex]∴ 6y² - 5y = 6∴ 6y² - 5y - 6 = 0 ⇒ factorize∴ (3y + 2)(2y - 3) = 0∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2∵ [tex]y=e^{x}[/tex]∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused   ([tex]e^{ax}[/tex] never gives -ve values)∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1∴ [tex]xlne=ln(3/2)[/tex] ∴ x = ln(3/2) = 0.41