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

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

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]
1
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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..

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

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

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 22 Jun 2017, 06:44.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:27, edited 1 time in total.
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Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink]
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]
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]
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.
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Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink]
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]
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]
$$8^{\frac{1}{2}} = 4^{x}$$

$$2^{\frac{3}{2}} = 2^{2x}$$

$$2x = \frac{3}{2}$$

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

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