Explanation
Recall that, \(\sin h x=e^{x}-e^{-x}\)
\(\therefore \frac{e^{x}-e^{-x}}{2}=1.475\)
Multiply both sides by 2 , we have
\(e^{x}-e^{-x}=2.95\)
Multiplying through by \(e^{x}\)
\begin{aligned}
&e^{2 x}-1=2.95 e^{x} \\
&\Rightarrow e^{2 x}-2.95^{x}-1=0 \\
&\text { Put } e^{x}=p \quad \ldots \ldots \ldots\left(c^{*}\right) \\
&\Rightarrow p^{2}-2.95 p-1=0
\end{aligned}
Using general formula for solving quadratic equation
\begin{aligned}
&P=\frac{2.95 \pm \sqrt{(-22.95)^{2}-4 \times 1}}{2} \\
&=\frac{2.95 \pm 3.5641}{2} \\
&\Rightarrow p=3.2571 \text { or }-0.3071
\end{aligned}
when \(p=-0.3071\) we haye from \((*)\) that \(=\)
\(e^{x}=-0.3071\). This is got posstible slrice exponential function is non negative.
When \(p=3.2571\) ine have from \(y\) ) that
\begin{aligned}
&e^{x}=3.2571 \\
&\Rightarrow x=\log (3.2+81)
\end{aligned}
\(1.1808\)