1)log7(8-x)=2
log7(8-x)=log7(7^2)
8-x=7^2
8-x=49
8-49=x
x=-41
2)log(1\6)(6-x)=-2
log(1\6)(6-x)=log(1\6)(1\6^(-2))
6-x=1\6^(-2)
6-x=36
-x=36-6
-x=30
x=-30
3)log2(7-x)=5
log2(7-x)=log2(2^5)
7-x=32
-x=32-7
-x=25
x=-25
4)log2(13-7x)=3*log2(3)
log2(13-7x)=log2(3^3)
13-7x=3^3
13-7x=27
-7x=27-13
-7x=14
x=-14\7
x=-2
5)lg(1\2+x)+lgx=lg1\2
lg((1\2+x)*x)=lg1\2
1\2*x+x^2=1\2
x^2+x\2-1\2=0
D=0,5^2-4*1*(-0,5)=0,25+2=2,25=1,5^2
x1=-0,5-1,5\2=-2\2=-1
x2=-0,5+1,5\2=1\2=0,5