Log1/3 (1+log3(2^x-7))=-1 решите плиз

Question

Log1/3 (1+log3(2^x-7))=-1 решите плиз

Answer 1

ОДЗ
{2^x-7>0⇒2^x>7⇒x>log(2)7
{1+log(3)(2^x-7))>0⇒log(3)(2^x-7)>-1⇒2^x-7>1/3⇒2^x>22/3⇒x>log(2)22/3
x∈(log(3)22/3;∞)
1+log(3)(2^x-7)=3
log(3)(2^x-7)=2
2^x-7=9
2^x=16
x=4