#### Answer

The value of the expression $30{{e}^{0.7x}}\le 240$ is $ x\le 2.97$.

#### Work Step by Step

We have to find the value of x from $30{{e}^{0.7x}}\le 240$ as given below:
$\begin{align}
& 30{{e}^{0.7x}}\le 240 \\
& {{e}^{0.7x}}\le 8 \\
& 0.7x\ln e\le \ln 8
\end{align}$
And simplify it further, to get:
$\begin{align}
& 0.7x\le 2.08 \\
& x\le 2.97
\end{align}$
Thus, the value of x is $ x\le 2.97$.