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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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22 Feb 2017, 02:46
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65% (hard)

Question Stats:

62% (02:31) correct 38% (02:35) wrong based on 120 sessions

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If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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Updated on: 22 Feb 2017, 21:29
5
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

$$2^{(8x)} = 640000 = 2^6*10^4$$
$$2^{(2x)} = 2^{6/4}*10^{4/4}$$
$$2^{(2x)} = 2^{3/2}*10$$
$$2^{(2x)} = 2\sqrt{2}*10 = 20\sqrt{2}$$

$$2^{(2x-2)} = 20\sqrt{2}/4 = 5\sqrt{2}$$

Hence Option A is correct
Hit Kudos if you liked it

Originally posted by 0akshay0 on 22 Feb 2017, 03:01.
Last edited by 0akshay0 on 22 Feb 2017, 21:29, edited 1 time in total.
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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22 Feb 2017, 05:59
In the step

2^(2x)=20√2 is OK

Now
2^(2x−2)=2^(2X) / 2^2 = 20√2 / 4 = 5√2
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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12 Jan 2018, 17:41
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 51307
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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12 Jan 2018, 23:20
1
rnz wrote:
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!

Step 1:

$$2^{(8x)} = 640000$$;

$$(2^{2x})^4 = 2^{10}*5^4$$;

$$2^{2x} = 2^{(\frac{5}{2})}*5$$;

$$2^{2x} = \sqrt{2^5}*5$$;

$$2^{2x} = 20\sqrt{2}$$.

Step 2:

$$2^{(2x−2)}=\frac{2^{(2x)}}{2^2}$$.

Step 2:

Substitute $$2^{2x} = 20\sqrt{2}$$ into $$\frac{2^{(2x)}}{2^2}$$.:

$$\frac{20\sqrt{2}}{2^2}=5\sqrt{2}$$.

Hope it's clear.
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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12 Jan 2018, 23:22
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Joined: 11 Sep 2015
Posts: 3243
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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13 Jan 2018, 06:01
2
Top Contributor
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

Another approach:

Given: 2^(8x) = 640000
Raise both sides to the power 1/2 (aka take square root of both sides) to get: [2^(8x)]^(1/2) = 640000^(1/2)
Simplify to get: 2^(4x) = 800
Raise both sides to the power 1/2 (again) to get: [2^(4x)]^(1/2) = 800^(1/2)
Simplify: 2^2x = √800
Simplify: 2^2x = 20√2
Divide both sides by 2² (aka 4) to get: (2^2x)/2² = (20√2)/4
Simplify both sides to get: 2^(2x - 2) = 5√2

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?  [#permalink]

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13 Jan 2018, 06:22
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

Another approach, although most of these approaches is solving the equation..

Let $$2^{(2x−2)}=y$$, so $$y^4=2^{(2x−2)*4}=2^{8x-8}=\frac{2^{8x}}{2^8}=\frac{640000}{2^6*2^2}=\frac{10000}{2^2}$$
so $$y^4=\frac{10000}{2^2}=\frac{10^4}{2^2}....y=\frac{10}{\sqrt{2}}=5\sqrt{2}$$

A
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If 2^(8x) = 640000, then what is the value of 2^(2x−2)? &nbs [#permalink] 13 Jan 2018, 06:22
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