logarithm: Solve [log_u(x−u)]^2 > 1 for all acceptable values of "u"

[Spaik]

logarithm: Solve [log_u(x−u)]^2 > 1 for all acceptable values of "u"

Can someone help me with this math problem?

Solve the inequality with all "u'' acceptable values.
[FONT=MathJax_Math-italic]log²_u[/FONT][FONT=MathJax_Main]([FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main])[/FONT][/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]1

[/FONT][FONT=MathJax_Math-italic]if u[FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main];[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main])[/FONT][/FONT], then x [FONT=MathJax_Main]∈
[/FONT][FONT=MathJax_Math-italic]if u[FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main];[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][/FONT], then x [FONT=MathJax_Main]∈

I have no idea how to get x, I have never solved anything like this[/FONT]

 

[Deleted member 4993]

Can someone help me with this math problem?

Solve the inequality with all "u'' acceptable values.
[FONT=MathJax_Math-italic]log²_u[/FONT][FONT=MathJax_Main]([FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main])[/FONT][/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]1[/FONT]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[Spaik]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

[FONT=MathJax_Math-italic]if u[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main];[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main])[/FONT], then x [FONT=MathJax_Main]∈
[/FONT][FONT=MathJax_Math-italic]if u[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main];[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT], then x [FONT=MathJax_Main]∈

I have no idea how to get x, I have never solved anything like this[/FONT]

 

[JeffM]

Consider this problem

\(\displaystyle log_u(v) > 1 \implies \text {WHAT about } v?\)

How about this problem

\(\displaystyle log_u(v) < -\ 1 \implies \text {WHAT about } v?\)

How about this one

\(\displaystyle log_u(v) > 1 \implies \text {WHAT about } log_u^2(v)?\)

And this one.

\(\displaystyle log_u(v) < -\ 1 \implies \text {WHAT about } log_u^2(v)?\)

Now put all that together.

\(\displaystyle log_u^2(v) > 1 \implies \text {WHAT about } v?\)

Answer these questions. Does that tell you how to solve your given problem