4^(x) -10•4^(-x) = 3?

4^x - 10(4^-x) = -3
4^x(4^x - 10(4^-x)) = 4^x(-3)
4^(2x) - 10 = -3(4^x)
4^(2x) + 3(4^x) - 10 = 0
Let u = 4^x.
u^2 + 3u - 10 = 0
(u + 5)(u - 2) = 0
u = -5 or u = 2
4^x = -5 or 4^x = 2
Discard 4^x = -5 because it has no real solutions, leaving just
4^x = 2
x = 1/2

let 4^x = y
---> y^2-3y-10=0
solve for y , then find x

y - 10/y = 3
y² - 3y - 10 = 0
[ y - 5 ] [ y + 3 ] = 0
y = 5 , y = - 3
4^x = 5
x log 4 = log 5
x = log 5 / log 4
x = 1.16

4^(x) – 10[4^(-x)] = 3
4^(x) – 10[1/(4^(x))] = 3

Let 4^(x) = y
y – 10/y = 3

Multiply both sides by y.
y² – 10 = 3y
y² –3y – 10 = 0
(y–5)(y+2) = 0

But y = 4^(x):
4^(x) – 5 = 0
4^(x) = 5
ln 4^(x) = ln 5
x = ln 5/ln 4 .................. [Ans]

4^(x) + 2 = 0
4^(x) = -2
x = undefined.

Therefore x=ln 5/ln 4.