Question

4^(x-2) - 3^x >=0 FInd the domain ??

Answer 1

First write
\[4^{x-2}\ge 3^{x}\]

Answer 2

then take logarithms on both sides and you have
\[(x-2)\ln 4\ge x \ln3\]

Answer 3

then you have
\[x (\ln4-\ln 3)\ge 2 \ln4\]

Answer 4

the imply
x>= ln 16/ ln(4/3) since ln 4-ln 3=ln (4/3) and 2 ln 4=ln 16

Answer 5

this imply x>=9.637

Answer 6

@Klevis