Verified answer

1) √7 - 5x = 8

5x = √7 - 8

x = (√7 - 8)/5

x ≑ - 1.07 (2.d.p)

2) Firstly, mulitply all the terms by e^x

e^x (e^x + 2) = e^x (8 e^(-x))

e^2x + 2e^x = 8e⁰

(e^x)^2 + 2e^x = 8

(e^x)^2 + 2e^x - 8 = 0

Now, just let y = e^x.... thus we can say y² = (e^x)²

y² + 2y - 8 = 0

(y + 4)(y - 2) = 0

y = - 4 or y = 2

Writing back in exponential form

e^x = - 4 or e^x = 2

Just ln both sides

ln e^x = ln - 4 or ln e^x = ln 2

ln - 4 (cannot be) so no solution for e^x = - 4 (since we are use real number system)

ln e^x = ln 2

x ln e = ln 2

x = (ln 2)/(ln e)

x = ln (2)

That's about it!