I need help with logarithms

[cherry00]

can you guys show me step by step how to do these? I have other exercises then.

 

[stapel]

I can't read the smallest characters on the first and third exercises. Please reply with typed-out versions.

When you reply, please show your thoughts and efforts so far. Thank you!

 

[cherry00]

\(\displaystyle 3\, \log_5(x\, -\, 4)\, >\, \dfrac{6}{\log_5(x\, -\, 4)\, +\, 1}\)

the 3 on the left goes away and the six of the right becomes a 2. Is it right?

 

[Ishuda]

\(\displaystyle 3\, \log_5(x\, -\, 4)\, >\, \dfrac{6}{\log_5(x\, -\, 4)\, +\, 1}\)

con you simplify the 3 on the left woth the six on the right?
the 3 on the left goes away and the 6 on the right turns into a 2?

Yes you can. If you then let
t = log₅(x-4)
you would have the equation
t > \(\displaystyle \frac{2}{t+1}\)
which might be easier to work with. It looks like you might want to consider two cases: (1) t > -1 and (2) t < -1. Note that t=-1 is excluded because the right hand side is not defined in that case.

After you get the answer in terms of t, translate it back to in terms of x.

 

[cherry00]

the right hand side is not defined in that case.

I don't understand this.

I think I get t ≠ -1 and t=1 and t=-2.

I get x>9 V x>(101/25)

and that's not what the book says
tha book says the result is
(101/25)<x<(21/5)Vx>9

How did he get this result?

Thank you very much for answering. I'll give you another exercise once you answer to this.

 

[stapel]

I don't understand this.

I think I get t ≠ -1 and t=1 and t=-2.

I get x>9 V x>(101/25)

Please reply showing your steps. Thank you!