Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

ln(x-2)+ln(2x-3)=2lnx

Sagot :

[tex]ln(x-2)+ln(2x-3)=2lnx\\\\D:x-2 > 0\ \wedge\ 2x-3 > 0\ \wedge\ x > 0\\x > 2\ \wedge\ x > 1.5\ \wedge\ x > 0\\x\in(2;\ \infty)[/tex]

[tex]ln[(x-2)(2x-3)]=lnx^2\\\\ln(2x^2-3x-4x+6)=lnx^2\\\\ln(2x^2-7x+6)=lnx^2\iff2x^2-7x+6=x^2\\\\2x^2-x^2-7x+6=0\\\\x^2-7x+6=0\\\\x^2-x-6x+6=0\\x(x-1)-6(x-1)=0\\(x-1)(x-6)=0\iff x-1=0\ \vee\ x-6=0\\\\x=1\notin D;\ x=6\in D\\\\Solution:x=6.[/tex]
konrad509
[tex]\ln(x-2)+\ln(2x-3)=2\ln x \\ D:x-2>0 \wedge 2x-3 >0 \wedge x>0\\ D:x>2 \wedge 2x>3 \wedge x>0\\ D:x>2 \wedge x>\frac{3}{2}\\ D:x>2\\ \ln(x-2)(2x-3)=\ln x^2\\ 2x^2-3x-4x+6=x^2\\ x^2-7x+6=0\\ x^2-x-6x+6=0\\ x(x-1)-6(x-1)=0\\ (x-6)(x-1)=0\\ x=6 \vee x=1\\ 1\not \in D\Rightarrow x=6 [/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.