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If x is different from zero and 64^3=8^x, then what is the value of
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24 May 2023, 05:44
24 May 2023, 05:44
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If x is different from zero and \(64^3=8^x\), then what is the value of \(x^2\) ?
A. 5
B. 6
C. 25
D. 36
E. 64
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A. 5
B. 6
C. 25
D. 36
E. 64
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) Cracking the GRE Premium
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Posts: 2506
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Re: If x is different from zero and 64^3=8^x, then what is the value of
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25 May 2023, 08:48
25 May 2023, 08:48
1
Expert Reply
To find the value of \(x^2\), we need to solve the given equation and find the value of x first.
We are given that \(64^3\) is equal to \(8^x:\)
\(64^3 = 8^x\)
We can rewrite 64 as \(8^2:\)
\((8^2)^3 = 8^x\)
Using the power of a power property, we can simplify the equation:
\(8^(2*3)\) = \(8^x\)
\(8^6 = 8^x\)
Since the bases are the same, the exponents must be equal:
\(6 = x\)
Now that we have found the value of x, we can substitute it into \(x^2:\)
\(x^2 = 6^2 = 36\)
Therefore, the value of \(x^2\) is 36.
So, the correct answer is D. 36.
We are given that \(64^3\) is equal to \(8^x:\)
\(64^3 = 8^x\)
We can rewrite 64 as \(8^2:\)
\((8^2)^3 = 8^x\)
Using the power of a power property, we can simplify the equation:
\(8^(2*3)\) = \(8^x\)
\(8^6 = 8^x\)
Since the bases are the same, the exponents must be equal:
\(6 = x\)
Now that we have found the value of x, we can substitute it into \(x^2:\)
\(x^2 = 6^2 = 36\)
Therefore, the value of \(x^2\) is 36.
So, the correct answer is D. 36.
gmatclubot
Re: If x is different from zero and 64^3=8^x, then what is the value of [#permalink]
25 May 2023, 08:48
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