Question

Логарифм который я не могу понять,спасити

Answer 1

$\lg^2(x) - \lg(x^2) + 1 = 6\\\lg^2(x) - 2\lg(x) + 1 = 6\\(\lg(x) - 1)^2 = 6\\(\lg(x) - 1 - \sqrt{6})(\lg(x) - 1 + \sqrt{6}) = 0\\x_1 = 10^{1 + \sqrt{6}}\\x_2 = 10^{1 - \sqrt{6}}$

Answer 2

$lg^{2}x-lgx^{2}+1=6\\\\lg^{2} x-2lgx-5=0\\\\lgx=m,x>0\\\\m^{2}-2m-5=0\\\\D=(-2)^{2} -4*(-5)=4+20=24=(2\sqrt{6})^{2}\\\\m_{1}=\frac{2+2\sqrt{6} }{2}=1+\sqrt{6}\\\\m_{2}=\frac{2-2\sqrt{6} }{2}=1-\sqrt{6}\\\\lgx=1+\sqrt{6} \\\\x_{1}=10^{1+\sqrt{6} }\\\\lgx=1-\sqrt{6}\\\\x_{2}=10^{1-\sqrt{6} }$