Question

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

Answer 1

If you meant `e^1 - 10x = 7 => x = (e-7)/10 =-0.42817` (5dp)

If you meant `e^(1 - 10x) = 7 => x = (1-ln7)/10 = -0.09459` (5dp)

Explanation:

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

Interpretation 1 : `\ \ e^1 - 10x = 7`

`:. e - 10x = 7`

`:. 10x = e-7`

`:. x = (e-7)/10`
`\ \ \ \ \ \ \ = -0.4281718 ...`
`\ \ \ \ \ \ \ = -0.42817` (5dp)

Interpretation 2 : `\ \ e^(1 - 10x) = 7`

`:. ln {e^(1 - 10x)} = ln7`

`:. 1-10x = ln7`

`:. 10x = 1-ln7`

`:. x = (1-ln7)/10`
`\ \ \ \ \ \ \ = -0.09459101 ...`
`\ \ \ \ \ \ \ = -0.09459` (5dp)