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

Question

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

sashiim20 · Answer

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

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

2x = \frac{3}{2}

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

Luckisnoexcuse · Answer

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

amastu · Answer

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?

Luckisnoexcuse · Answer

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

shashankism · Answer

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...

shashankism · Answer

How did you cancelled 2 from both sides ??. We can't cancel 2 like this

BrentGMATPrepNow · Answer

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

Answer: C

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shashankism · Answer

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...

shashankism · Answer

mynamegoeson  
 8^{(\frac{1}{2})}  is not equal to 64^(2/2) . it is equal to 64^(1/4)

Bunuel · Answer

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

shashankism · Answer

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..

pushpitkc · Answer

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})}

TimeTraveller · Answer

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

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

2x = \frac{3}{2}

x = \frac{3}{4} . Ans - C.

JeffTargetTestPrep · Answer

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

Demonicgod · Answer

Step 1: Simplify left-hand side 
81/2=8=4⋅2=228^{1/2} = \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}81/2=8=4⋅2=22
 
 Step 2: Express both sides in base 2 
81/2=(23)1/2=23/28^{1/2} = (2^3)^{1/2} = 2^{3/2}81/2=(23)1/2=23/2 4x=(22)x=22x4^x = (2^2)^x = 2^{2x}4x=(22)x=22x
 
 Step 3: Equating exponents (same base) 
23/2=22x2^{3/2} = 2^{2x}23/2=22x 32=2x\frac{3}{2} = 2x23=2x x=34x = \frac{3}{4}x=43
 
✅  Answer: C. 3/4

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?

Prep Toolkit

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