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Find the number of solutions of following equation-: ||x|-6|=2^x

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Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 05:29
1
12
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

12% (01:52) correct 88% (01:58) wrong based on 102 sessions

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Find the number of solutions of following equation-:
\(||x|-6|=2^x\)

A. 0
B. 1
C. 2
D. 3
E. 4
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Senior Manager
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Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 18:25
7
2
Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

Posted from my mobile device
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Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 07:51
1
nick1816 wrote:
Find the number of solutions of following equation-:
\(||x|-6|=2^x\)

A. 0
B. 1
C. 2
D. 3
E. 4


only x=2 satisfies so answer should be B i think

PFA the image

I am not clear on how to check for fractions in these equations.
nick1816 can u please help
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Senior Manager
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Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 21:02
1
vanam52923 wrote:
can u explain the last graph ,how did u find intersecting point of 2^x nd other graph


Hi Peddi and vanam52923

That's the characteristic of line y=2^x that the line increases exponentially --if X goes further to the right-- and decreases slowly --if Z goes to the left--, but Y is never negative and not even touches 0. Therefore, the line y=2^x will eventually intersect TWICE with the absolute line (points A and B) on negative X range.

Draw both lines on you sketch and you may understand better what I mean above
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Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 20:30
chondro48 wrote:
Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

Posted from my mobile device

can u explain the last graph ,how did u find intersecting point of 2^x nd other graph
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Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 04 Sep 2019, 20:51
chondro48 wrote:
Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

Posted from my mobile device

Can you explain the fourth graph breifly
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Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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New post 14 Sep 2019, 05:54
1
This one is completely over my head I tend to use more sophisticated and simple approaches (the methodical apporach) Can I have your take on this one? Bunuel

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Re: Find the number of solutions of following equation-: ||x|-6|=2^x   [#permalink] 14 Sep 2019, 05:54
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