Question

How do you solve `3e^x+1=5`?

Answer 1

`x≈0.2877" to 4 dec. places"`

Explanation:

Begin by expressing the equation in terms of `e^x.`

`3e^x=4rArre^x=4/3`

Take ln (natural logarithm) of both sides.

`rArrlne^x=ln(4/3)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(loga^xhArrxloga)color(white)(2/2)|)))`

`rArrxcancel(lne)^1=ln(4/3)`

`rArrx=ln(4/3)≈0.2877" to 4 dec. places"`