Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Join our knowledgeable community and get detailed, reliable answers to all your questions.

 If log3x – log3(x + 1) = 2log33, then x =

Sagot :

Kate200468idn
[tex]1)\ \ \ log_3x-log_3(x + 1) = 2log_33\ \ \ \Rightarrow\ \ \ D:x>0\ \ \ and\ \ \ x+1>0\\. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=(0;+\infty)\\\\log_3 \frac{x}{x+1} =log_33^2\ \ \ \Leftrightarrow\ \ \ \ \frac{x}{x+1}=9\ /\cdot(x+1)\\\\x=9(x+1)\\\\x=9x+9\\\\-8x=9\ \ \ \Leftrightarrow\ \ \ x=- \frac{9}{8} \ \notin\ D\ \ \ \Rightarrow\ \ \ no\ solution\\\\[/tex]

[tex]2)\ \ \ log3x-log3(x + 1) = 2log33\ \ \ \Rightarrow\ \ \ D:x>0\ \ \ and\ \ \ x+1>0\\. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=(0;+\infty)\\\\log \frac{3x}{3(x+1)} =log33^2\ \ \ \Leftrightarrow\ \ \ \frac{x}{(x+1)} =1089\ /\cdot(x+1)\\\\x=1089(x+1)\\\\x=1089x+1089\\\\x-1089x=1089\\\\-1088x=1089\ /:(-1088)\\\\x=- \frac{1089}{1088} \ \notin\ D\ \ \ \Rightarrow\ \ \ no\ solution\\\\Ans.\ the\ equation\ has\ no\ solution.[/tex]
[tex]log3x-log3(x+1)=2log33\ (*)\\\\D:3x > 0\ \wedge\ x+1 > 0\\\\x > 0\ \wedge\ x > -1\\\\D:x\in\mathbb{R^+}\\\\(*)\ log\frac{3x}{3(x+1)}=log33^2\iff \frac{x}{x+1}=1089\\\\1089(x+1)=x\\\\1089x+1089-x=0\\\\1088x=-1089\ \ \ \ /:1088\\\\x=-\frac{1089}{1088}\notin D\\\\Answer:no\ solution;\ x\in\O.[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.