Question

Question #c2837

Answer 1

`x=color(green)(1/2)`

Explanation:

If
`color(white)("XXX")10xe^x-5e^x=0`
since
`color(white)("XXX")e^"any power" > 0`

We can divide (both sides of)the given equation by `5e^x` to get
`color(white)("XXX")2x-1=0`

From which we can see that
`color(white)("XXX")x=1/2`

Answer 2

`x=1/2`

Explanation:

There is a common factor of `e^x` which can be taken out.

`rArre^x(10x-5)=0`

`rArre^x=0,10x-5=0`

but `e^x≠0" thus no solution"`

and `10x-5=0rArrx=1/2" is the only solution"`