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If 8^(1/2) = 4^x, what is the value of x?

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If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post Updated on: 22 Jun 2017, 07:49
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Originally posted by Bunuel on 22 Jun 2017, 05:34.
Last edited by Bunuel on 22 Jun 2017, 07:49, edited 1 time in total.
Edited the options.
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If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post Updated on: 22 Jun 2017, 08:04
1
\(8^{(\frac{1}{2})} = 4^x\)

\(2^{(\frac{3}{2})}= (2)^{2x}\)

\(2x = \frac{3}{2}\)

\(x = \frac{3}{4}\) . Answer (C)...

Originally posted by sashiim20 on 22 Jun 2017, 05:44.
Last edited by sashiim20 on 22 Jun 2017, 08:04, edited 1 time in total.
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:24
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^(1/2)\) = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:30
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8^(1/2)=4^x
2^(3/2) =2^(2x)
3/2 = 2x
x= 3/4

Bunuel, did I make a mistake or are the answers incorrect?
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post Updated on: 22 Jun 2017, 06:53
1
mynamegoeson wrote:
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^(1/2)\) = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong



Let me correct myself

\(8^{(\frac{1}{2})} = 4^x\)
We can write it as
64^(1/4) = 64^(x/3)

x/3 = 1/4
x=3/4
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Originally posted by Luckisnoexcuse on 22 Jun 2017, 06:35.
Last edited by Luckisnoexcuse on 22 Jun 2017, 06:53, edited 1 time in total.
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:42
1
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


Bunuel why so many questions posted today has wrong options.. This question also has none of the options matching with the correct answer..

Please check the options again.
As for the solution .. \(8^{(\frac{1}{2})} = 4^x\)
-> 2^(3/2) = 2 ^(2x)
-> 3/2 = 2x
-> x = 3/4

No options is matching the answer...
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:43
1
sashiim20 wrote:
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^{(\frac{1}{2})} = 4^x\)

\(\sqrt{2^3} = (2*2)^x\)

\(2\sqrt{2} = (2*2)^x\)

Cancelling 2 from both sides we get;

\(\sqrt{2} = (2)^x\)

\(2^{(\frac{1}{2})} = 2^x\)

\(x = \frac{1}{2}\) . Answer (A) ...


How did you cancelled 2 from both sides ??. We can't cancel 2 like this
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:44
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Top Contributor
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


Given: \(8^{(\frac{1}{2})} = 4^x\)

Rewrite 8 as 2³ and 4 as 2² to get: (2³)^(1/2) = (2²)^x
Apply power of a power law to both sides: 2^(3/2) = 2^(2x)
So, we can conclude that 3/2 = 2x
Divide both sides by 2 to get: 3/4 = x

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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:46
mynamegoeson wrote:
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^(1/2)\) = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong


I don't think we can work with closest value.. No approximation is asked in question.
Also approximating 2.83 to 2 is not the right way of solving quantitative questions.. We must keep in mind that approximation should look like approximation.. I think here the options are wrong...
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 06:49
mynamegoeson wrote:
mynamegoeson wrote:
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^(1/2)\) = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong



Let me correct myself

\(8^{(\frac{1}{2})} = 4^x\)
We can write it as
64^(2/2) = 64^(x/3)

x/3 = 1
x=3
Hence option D


mynamegoeson
\(8^{(\frac{1}{2})}\) is not equal to 64^(2/2) . it is equal to 64^(1/4)
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 07:53
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 08:05
Bunuel wrote:
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1


Apologise to all of you. Copied options of another question here. Edited.


No issues Bunuel .. You are doing great work.. You have posted so many questions on daily basis. So sometimes you might get confused with options.. Humans :)
But your work is helping us a lot in preparation of Quant. Keep up the good work..
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If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 09:02
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?


Since \(8^{(\frac{1}{2})} = 2*\sqrt{2}\)

We have to find which value of x makes \(4^x = 2*\sqrt{2}\)

Of the available options, \(x=\frac{3}{4}\)(Option C) makes

\(4^x = 4^{\frac{3}{4}} = (4*4*4)^{\frac{1}{4}} = 2*\sqrt{2} = 8^{(\frac{1}{2})}\)
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 09:23
\(8^{\frac{1}{2}} = 4^{x}\)

\(2^{\frac{3}{2}} = 2^{2x}\)

\(2x = \frac{3}{2}\)

\(x = \frac{3}{4}\). Ans - C.
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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New post 24 Jun 2017, 08:30
Bunuel wrote:
If \(8^{(\frac{1}{2})} = 4^x\), what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1


Lets simplify the given equation and determine x:

8^(½) = 4^x

(2^3)^½ = 2^2x

2^3/2 = 2^2x

3/2 = 2x

x = 3/4

Answer: C
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Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

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Re: If 8^(1/2) = 4^x, what is the value of x?   [#permalink] 05 Feb 2019, 07:25
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