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Bunuel
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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 07:48
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B
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94% (00:25) correct 6% (00:37) wrong based on 64 sessions

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If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4
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B
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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 07:50
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8^1/3=2 and 2^2 =4.. Therefore x=1

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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 07:54
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4


\(8^{(\frac{2}{3})} = 4^x\)
-> 2^2 = 2^2x

-> 2x = 2
-> x=1

Answer B
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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 07:56
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

Given: \(8^{(\frac{2}{3})} = 4^x\)

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

Answer:
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B

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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 07:57
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

\(8^{(\frac{2}{3})} = 4^x\)

\((2^3)^{(\frac{2}{3})} = 4^x\)

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

\(2x =2\)

\(x = 1\) . Answer (B) ...
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If 8^(2/3) = 4^x, what is the value of x? 22 Jun 2017, 12:13
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4
\(8^{(\frac{2}{3})} = 4^x\)

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

Distribute the exponent inside the parentheses on both sides, (i.e. multiply the exponent inside parentheses by every exponential term outside parentheses):

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

\(2^{(\frac{6}{3})} = (2)^{2x}\)

Base on both sides is identical. Set exponents equal to each other (LHS exponent is \(\frac{6}{3}\)= 2):

2 = 2x

x = 1

Answer
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B
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If 8^(2/3) = 4^x, what is the value of x? 23 Jun 2017, 08:55
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

\(8^{(\frac{2}{3})} = 4^x\)

Or, \(2^{(\frac{2*3}{3})} = 2^{2x}\)

Or, \(2^2 = 2^{2x}\)

So, \(2x = 2\)

Or, \(x = 1\)

Thus, answer must be (B) 1
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If 8^(2/3) = 4^x, what is the value of x? 23 Jun 2017, 11:06
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8^(2/3) = 4^x,
8 = 2^3,
Therefore,
8^(2/3) = 2^(3*2/3) = 2^(2) = 4^1,
4^1 = 4^x,
x = 1
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If 8^(2/3) = 4^x, what is the value of x? 23 Jun 2017, 12:17
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\(8^{(\frac{2}{3})} = 4^x\)

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


\(2 = 2x\)

\(x = 1\)


Hence, Answer is B = 1
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If 8^(2/3) = 4^x, what is the value of x? 26 Jun 2017, 17:53
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Bunuel
If \(8^{(\frac{2}{3})} = 4^x\), what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

Let’s simplify the given equation. We first express each side of the equation with the same base. Then we equate the exponents.

8^(⅔) = 4^x

(2^3)^(⅔) = 2^2x

2^2 = 2^2x

2 = 2x

x = 1

Answer: B
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