# What are the solutions of the equation e^1-10x = 7?

Mar 1, 2017

If you meant ${e}^{1} - 10 x = 7 \implies x = \frac{e - 7}{10} = - 0.42817$ (5dp)

If you meant ${e}^{1 - 10 x} = 7 \implies x = \frac{1 - \ln 7}{10} = - 0.09459$ (5dp)

#### Explanation:

There is an ambiguity in the way you have written the expression

Interpretation 1 : $\setminus \setminus {e}^{1} - 10 x = 7$

$\therefore e - 10 x = 7$

$\therefore 10 x = e - 7$

$\therefore x = \frac{e - 7}{10}$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus = - 0.4281718 \ldots$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus = - 0.42817$ (5dp)

Interpretation 2 : $\setminus \setminus {e}^{1 - 10 x} = 7$

$\therefore \ln \left\{{e}^{1 - 10 x}\right\} = \ln 7$

$\therefore 1 - 10 x = \ln 7$

$\therefore 10 x = 1 - \ln 7$

$\therefore x = \frac{1 - \ln 7}{10}$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus = - 0.09459101 \ldots$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus = - 0.09459$ (5dp)