Question

Please help me solve 4^x - 2^x - 12 = 0

Answer 1

Hint:

Let z = 2^x

so z^2 = (2^x)^2 ---> z^2 = 4^x

Answer 2

which means you can turn

4^x - 2^x - 12 = 0

into

z^2 - z - 12 = 0

Answer 3

x = 2

Answer 4

x = 6 or x = 2 ? I got x = 6 is my result correct?

Answer 5

you would then solve for z

once you get your two solutions for z, you would use them to find the solution for x

Answer 6

when you solve z^2 - z - 12 = 0 for z, you get

z = 4

z = -3

Answer 7

ignore the -3 since 2^x is always positive

Answer 8

so

z = 2^x

4 = 2^x

x = ???

Answer 9

2 :(

Answer 10

yep