solve the equations for x

Question

a) e^2x - e^x - 30 = 0

b)1-3/n^x = 5

Answer 1

let z = e^x
then
z^2 - z - 30 = 0
(z-6)(z+5) = 0
so
z = 6 or -5
if z = e^x = 6
x = ln 6 look it up
if z = -5
x = ln -5 impossible so only ln 6 is solution

Answer 2

Are you sure this is not a typo?

1-3/n^x = 5

-3/n^x = 4

n^x = -3/4
ln n^x = -ln .75
x ln n = -ln.75
x = -ln.75/ln n
x = .2877/ln n