Question

Solve the following inequalities.
$2^x+3^x⩾2.$

Answer 1

We know that -

For $x<0$ ,

$3^x<2^x<1$

For $x=0$ ,

$3^x=2^x=1$

For $x>0$ ,

$3^x>2^x>1$

Hence, $2^x+3^x\ge 1$ when $x\ge 0$

Solution set is - $x\in [0,\infty )$