Value of x is 0.29
Step-by-step explanation:
We have equation 6eˣ -4e⁻ˣ = 5
Multiplying throughout by eˣ
We will get
[tex]6e^x\times e^x-4e^{-x}\times e^x=5\times e^x\\\\6e^{2x}-4=5e^x\\\\6e^{2x}-5e^x-4=0[/tex]
Substitute eˣ = y
6y² - 5y - 4 = 0
[tex]y=\frac{-(-5)\pm \sqrt{(-5)^2-4\times 6\times (-4)}}{2\times 6}=\frac{5\pm \sqrt{121}}{12}=\frac{5\pm 11}{12}\\\\y=\frac{16}{12}=\frac{4}{3}\texttt{ or }y=\frac{-6}{12}=\frac{-1}{2}[/tex]
That is
[tex]e^x=\frac{4}{3} \texttt{ or }e^x=\frac{-1}{2}\\\\x=log\left ( \frac{4}{3}\right ) \texttt{ or }x=log\left ( \frac{-1}{2}\right )\Rightarrow \texttt{Not possible}\\\\x=0.29[/tex]
Value of x is 0.29
