помогите решить?!! 1) lg^2 x -lg ^2 (10x)= 2) 6-lg^2 (100x)=

Question 1

помогите решить?!!

1) lg^2 x -lg ^2 (10x)=

2) 6-lg^2 (100x)=

Question 2

$lg^2 x-lg^2 {10 x}=(lg x-lg (10x))(lg x+lg(10x))=lg \frac{x}{10x} lg (x*10x)=lg \frac{1}{10} *lg (10x^2)=lg 10^{-1} *(lg (10)+lg (x^2))=-1*(1+2lg x)=-1-2lg x$

$6-lg^2 {100x}=6-(lg 100+lg x)^2=6-(2+lg x)^2=6-4-4lg x-lg^2 x=-lg^2 x-4lg x+2$

0; 10x>0; 100x>0;\\ x>0;\\ -1-2lg x=-lg^2 -4lg x+2;\\ lg^2 x+4lg x-2lg x-1-2=0;\\ lg^2 x+2lg x-3=0;\\ (lg x+3)*(lg x-1)=0;\\\\ lg x+3=0;\\ lg x=-3;\\ x_1=10^{-3}=0.001;\\\\ lg x-1=0;\\ lg x=1; x_2=10^1=10; x_1*x_2=0.001*10=0.01" alt="lg^2 x-lg^2 (10x)=6-lg^2 (100x)=0;\\ x>0; 10x>0; 100x>0;\\ x>0;\\ -1-2lg x=-lg^2 -4lg x+2;\\ lg^2 x+4lg x-2lg x-1-2=0;\\ lg^2 x+2lg x-3=0;\\ (lg x+3)*(lg x-1)=0;\\\\ lg x+3=0;\\ lg x=-3;\\ x_1=10^{-3}=0.001;\\\\ lg x-1=0;\\ lg x=1; x_2=10^1=10; x_1*x_2=0.001*10=0.01" align="absmiddle" class="latex-formula">

dtnth_zn · Answer 1 · 2018-03-05T13:12:17+0000

$lg^2 x-lg^2 {10 x}=(lg x-lg (10x))(lg x+lg(10x))=lg \frac{x}{10x} lg (x*10x)=lg \frac{1}{10} *lg (10x^2)=lg 10^{-1} *(lg (10)+lg (x^2))=-1*(1+2lg x)=-1-2lg x$

$6-lg^2 {100x}=6-(lg 100+lg x)^2=6-(2+lg x)^2=6-4-4lg x-lg^2 x=-lg^2 x-4lg x+2$

0; 10x>0; 100x>0;\\ x>0;\\ -1-2lg x=-lg^2 -4lg x+2;\\ lg^2 x+4lg x-2lg x-1-2=0;\\ lg^2 x+2lg x-3=0;\\ (lg x+3)*(lg x-1)=0;\\\\ lg x+3=0;\\ lg x=-3;\\ x_1=10^{-3}=0.001;\\\\ lg x-1=0;\\ lg x=1; x_2=10^1=10; x_1*x_2=0.001*10=0.01" alt="lg^2 x-lg^2 (10x)=6-lg^2 (100x)=0;\\ x>0; 10x>0; 100x>0;\\ x>0;\\ -1-2lg x=-lg^2 -4lg x+2;\\ lg^2 x+4lg x-2lg x-1-2=0;\\ lg^2 x+2lg x-3=0;\\ (lg x+3)*(lg x-1)=0;\\\\ lg x+3=0;\\ lg x=-3;\\ x_1=10^{-3}=0.001;\\\\ lg x-1=0;\\ lg x=1; x_2=10^1=10; x_1*x_2=0.001*10=0.01" align="absmiddle" class="latex-formula">