4)
1. (lgb*2*^(lg₂lgb)¹/²*(lgb²)⁻¹/²=(lgb*lgb)¹/²=(√lg²b)/√lgb²=lgb/√(2*lgb).
2. √((lg²b+1)/(2*lgb)+1)=√((lg²b+2*lgb+1)(2*lgb))=√((lgb+1)²/(2*lgb))=
=(lgb+1)/√(2*lgb).
3.10^((1/2)*lglgb¹/²)=10^(lg√lgb¹/²)=√lgb¹/²=√(lgb/2).
4. (lgb+1)/√(2*lgb)-√(lgb/2)=(lgb+1-√(2*lgb*lgb/2))/√(2*lgb)=
=(lgb+1-√lgb²)/(2*lgb)=(lgb+1-lgb)/√(2*lgb)=1/(2*lgb).
5. (lgb/√(2*lgb)/(1/√(2*lgb)=lgb.
5)
log₆15=a log₆12=b log₂₅6-?
a+b=log₆15+log₆12=log₆180=log₆(36*5)=log₆36+log₆5=log₆6²+log₆5=
2*log₆6+log₆5=2+log₆5
log₆5=a+b-2 "|×2
2*log₆5=2a+2b-4
log₆25=2a+2b-4
log₂₅6=1/(2a+2b-4).