Solve for X: (16^x)-12*4^x=-35?

Question

Needs to solved in terms of ln, natural log

Answer 1

4^(2x) - 12*4^x = -35

I am going to substitute A for 4^x, then

A^2 - 12A + 35 = 0
(A - 7)(A - 5) = 0
So either A = 7 or A = 5

So 4^x =7 or 4^x = 5
and
ln 4^x = ln 7 or ln 4^x = ln 5
x ln4 = ln 7 or x ln4 = ln5

x = (ln7)/(ln4) or x = (ln5)/(ln4)

Piece of cake!

Answer 2

Natural logs wont hack it, since you have an subtraction. However, you can rewrite this as
4^2x - 12 (4^x) + 35 = 0
Let U= 4^x and you have U^2 - 12U+35=0
I think you can see where this is going.

Answer 3

Let 4^x = u

u^2 - 12u = -35

u^2 - 12u + 35 = 0

(u-7)(u-5) = 0

u = 7

u = 5

4^x = 5

log base (4) 5 = x

log base (4) 7 = x

Answer 4

(4^2x)-12(4^x)+35=0
(4^x)^2-12(4^x)+35=0
let 4^x=a
a^2-12a+35=0
(a-5)(a-7)=0
a=5 or 7
when a=5, 4^x=5
xln4=ln5
x=(ln5/ln4)
=1.16
when a=7, 4^x=7
xln4=ln7
x=(ln7/ln4)
=1.40