Identities for solving log questions

[I like Serena]

Hi Pranav-Arora!

Thanks!It worked!

My next question:-

$$\log_3\frac{|x^2-4x|+3}{x^2+|x-5|} \ge 0$$

Hmm, that's not a question - it's a problem.
What is your question?

I suspect that the log should bother you no more by now, nor the matter of the domain of the log function.

The only new thing is the absolute value function...
And I'm not sure whether you fully understand when an inequality inverts and how exactly...

Perhaps show a few steps...?

 

[Saitama]

Hi Pranav-Arora!



Hmm, that's not a question - it's a problem.
What is your question?

I suspect that the log should bother you no more by now, nor the matter of the domain of the log function.

The only new thing is the absolute value function...
And I'm not sure whether you fully understand when an inequality inverts and how exactly...

Perhaps show a few steps...?

When i tried to solve it, i wasn't able to go further than this:-

$$\frac{|x^2-4x|+3}{x^2+|x-5|} \ge 1$$

I am not able to figure out what should i do next?

 

[I like Serena]

When i tried to solve it, i wasn't able to go further than this:-

$$\frac{|x^2-4x|+3}{x^2+|x-5|} \ge 1$$

I am not able to figure out what should i do next?

What would happen if you multiplied left and right by the denominator?

Can you separate this in a number of cases for x?
That is, for instance, what would the signs of the absolute values be if x > 5?
For which values of x would one or the other absolute value invert its sign?

 

[I like Serena]

When i tried to solve it, i wasn't able to go further than this:-

$$\frac{|x^2-4x|+3}{x^2+|x-5|} \ge 1$$

I am not able to figure out what should i do next?

What would happen if you multiplied left and right by the denominator?

Can you separate this in a number of cases for x?
That is, for instance, what would the signs of the absolute values be if x > 5?
For which values of x would one or the other absolute value invert its sign?

 

[Saitama]

What would happen if you multiplied left and right by the denominator?

Can you separate this in a number of cases for x?
That is, for instance, what would the signs of the absolute values be if x > 5?
For which values of x would one or the other absolute value invert its sign?

Absolute values are positive only...so why are you asking me "what would the signs of the absolute values be if x > 5?"

 

[I like Serena]

Absolute values are positive only...so why are you asking me "what would the signs of the absolute values be if x > 5?"

What I meant is that you can write an absolute value without the vertical bars if you put the appropriate sign before it in combination with a domain restriction.

For instance:
|x-5| = (x-5) if x > 5
|x-5| = -(x-5) if x < 5

 

[ehild]

Look at the denominator. Can it be negative?

ehild