Question

help solve: e^x(e^x - 5) = -4

Answer 1

\[e^x(e^x - 5) = -4\]
and then I went to:
\[(e^x)^2 - 5(e^x) = -4\]

but I feel like I'm on the wrong path. Please help!

Answer 2

you're on the right track.

next step:\[e^{2x} - 5e^x + 4= 0\]and like a polynomial, you can factor it:\[(e^x - 4)(e^x - 1) = 0\]

zero product rule: 0 when e^x = 4 or e^x = 1

x = ln(4) or ln(1)

Answer 3

thanks! how did you get x = ln4 or ln1 though?

Answer 4

\[e^x = 4\]\[\ln(e^x) = \ln(4)\]
and \[\ln(e^x) = x\]

LN is the inverse operation of the exponential function. you can also play around and test with your calculator to confirm this

Answer 5

thank you :)

Answer 6

glad i could help :)

let me know if you have follow-up questions :)