Let me do it all the way to avoid too much asking/answering if in case.

4^x - 10 * 4^-x = 3

If that is

(4^x) -10(4^(-x)) = 3,

then,

4^x -10/(4^x) = 3

Clear the fraction, multiply both sides by 4^x,

4^(x+x) -10 = 3(4^x)

4^(2x) -3(4^x) -10 = 0

That is a quadratic equation in 4^x,

[if y = 4^x, then that is y^2 -3y -10 = 0]

so, factoring it,

(4^x -5)(4^x +2) = 0

When 4^x -5 = 0,

4^x = 5

Take the common logs of both sides,

xLog(4) = Log(5)

x = log(5) / Log(4)

x = 1.160964047 ---------------answer.

When 4^x +2 = 0,

4^x = -2

Take the common logs of both sides,

xLog(4) = Log(-2)

There are no real number logs of negative numbers, so reject 4^x +2 = 0.