10.50lg(x-1)=a3a²-10a+3=0D=100-36=64, √D=8a1=(10-8)/6=1/3⇒lg(x-1)=1/3⇒x-1=∛10⇒x=1+∛10a2=(10+8)/6=3⇒lg(x-1)=3⇒x-1=1000⇒x=100110.52(2+lgx)²+(1+lgx)²=14-lgx4+2lgx+lg²x+1+2lgx+lg²x-14+lgx=02lg²x+7lgx-9=0lgx=a2a²+7a-9=0D=49+72=121, √D=11a1=(-7-11)/4=-4⇒lgx=-4⇒x=0,0001a2=(-7+11)/4=1⇒lgx=1⇒x=1010.544lgx-(lg(-x))²=4ОДЗ x>0 U -x>0⇒x>0 U x<0- нет решения10.564log²(2)(x-1)+log(2)(x-1)-5=0log(2)(x-1)=a4a²+a-5=0D=1+80=81, √D=9a1=(-1-9)/8=-5/4⇒log(2)(x-1)=-5/4⇒x-1=2^-5/4=1/2
![\sqrt[4]{2} \sqrt[4]{2}](https://tex.z-dn.net/?f= \sqrt[4]{2} )
⇒x=1+1/2
![\sqrt[4]{2} \sqrt[4]{2}](https://tex.z-dn.net/?f= \sqrt[4]{2} )
a2=(-1+9)/8=1⇒log(2)(x-1)=1⇒x-1=2⇒x=310.58(log(1/2)4+log(1/2)x)²+log(2)x-log(2)8=8(log(1/2)x-2)²-2log(1/2)x-3-8=0log²(1/2) x-4log(1/2)x+4-2log(1/2)x-3-8=0log²(1/2) x-6log(1/2)x-7=0log(1/2)x=aa²-6a-7=0⇒a1+a2=6 U a1*a2=-7a1=7⇒log(1/2)x=7⇒x=1/128a2=-1⇒log(1/2)=-1⇒x=210.60(lgx+1)(lgx-1)=3lgx-3lg²x-1-3lgx+3=0lg²x-3lgx+2=0lgx=aa²-3a+2=0⇒a1+a2=3 U a1*a2=2a1=2⇒lgx=2⇒x=100a2=1⇒lgx=1⇒x=1010.62(1-4lg²x)/(lgx-2lg²x)=4lgx+5(1-2lgx)(1+2lgx)/lgx(1-2lgx)=4lgx+5(1+2lgx)/lgx=4lgx+51+lgx=lgx(4lgx+5), x≠√104lg²x+5lgx-2lgx-1=04lg²x+3lgx-1=0lgx=a4a²+3a-1=0D=9+16=25,√D=5a1=(-3-5)/8=-1⇒lgx=-1⇒x=0,1a2=(-3+5)/8=1/4⇒lgx=1/4⇒x=
![\sqrt[4]{10} \sqrt[4]{10}](https://tex.z-dn.net/?f= \sqrt[4]{10} )
10.64(1+log(2)x)²-4log(2)x=01+2log(2)x+log²(2)x-4log(2)x=01-2log(2)x+log²(2)x=0(1-log(2)x)²=01-log(2)x=0log(2)x=1x=2