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log по основанию sqrt(2) числа (x+4) меньше или равно 2

Guest Feb 7, 2015

Best Answer 

 #7
avatar+88898 
+5

Here's another way

log√2(x + 4) ≤ 2

This says that

(√2)^2 ≥ x + 4    and, remembering that x + 4 > 0   ....so we have

2 ≥ x + 4          and      x + 4 > 0

-2 ≥ x               and      x > -4

So, the solution is

(-4, -2]  for x   ...note that -2 is included because (√2)^2  ≤ (-2 + 4)   ....

 

CPhill  Feb 7, 2015
 #1
avatar+93351 
+5
 




log on the base of sqrt ( 2 ) numbers ( x +4 ) is less than or equal to 2

 

 

$$\\\sqrt{x+4}\le 2\\\\
(\sqrt{x+4})^2\le 2^2\\\\
x+4\le 4\\\\
x+4-4\le 4-4\\\\
x\le 0\\\\$$



Melody  Feb 7, 2015
 #2
avatar+752 
+3

what's the meaning of that question???

Sasini  Feb 7, 2015
 #3
avatar+11847 
0

translator.......

 

 

i mean check in the translator!

 

rosala  Feb 7, 2015
 #4
avatar+93351 
+5

You know Sasini, I do not think I answered the intended question.

I might try it again.  (It is written in Russian)

I use Bing or Google translators to make sense of these.

 

logonthe base ofsqrt (2)numbers (x+4)is less than or equal to2
 
 
$$\\log_{\sqrt{2}}\;(x+4)\le 2\\\\
\sqrt{2}^{(log_{\sqrt{2}}\;(x+4))}\le\sqrt{2}^ 2\\\\
(x+4)\le 2\\\\
x\le -2\\\\$$
 
But you can only find the log of a positive number so
 
$$\\x+4>0\\
x>-4\\\\
Hence\\\\
-4 or \\
$alternatively the domain is $ (-4,-2)$$
Melody  Feb 7, 2015
 #5
avatar+93351 
+5

I might try looking at this question a more straight forward way.

 

$$\\NOTE: \;\;x+4>0\;\;so\;\;x>-4\\\\
log_{\sqrt2}(x+4)\le2\\\\
\frac{log(x+4)}{log{\sqrt2}}\le2\\\\
log(x+4)\le 2log\sqrt2\\\\
log(x+4)\le 2log(2^{1/2})\\\\
log(x+4)\le log(2)\\\\
x+4\le2\\\\
x \le -2\\\\
therefore\qquad -4

 

slight errors corrected - thanks Chris :))

Melody  Feb 7, 2015
 #6
avatar+93351 
+5
Melody  Feb 7, 2015
 #7
avatar+88898 
+5
Best Answer

Here's another way

log√2(x + 4) ≤ 2

This says that

(√2)^2 ≥ x + 4    and, remembering that x + 4 > 0   ....so we have

2 ≥ x + 4          and      x + 4 > 0

-2 ≥ x               and      x > -4

So, the solution is

(-4, -2]  for x   ...note that -2 is included because (√2)^2  ≤ (-2 + 4)   ....

 

CPhill  Feb 7, 2015
 #8
avatar+93351 
0

Yes I like that Chris, thanks.

Melody  Feb 7, 2015

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