Question

log2 (6+x) <  3 
5^((x^2) - 15) = 25^x
sinx=2 cosx

Answer 1

1)log₂(6+x)<3
log₂(6+x)<log₂8
0<6+x<8
-6<x<2
x∈(-6;2)
$2)5^{ x^{2} -15}=25^{x} \ 5^{ x^{2} -15}=5^{2x} \ x^{2} -15=2x \ x^{2} -2x-15=0 \ D=64;x_{1}=5;x_{2}=-3 \ 3)sinx=2cosx (:cosx neq 0) \ tgx=2 \ x=arctg2+ pi k$
k∈Z