GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If x is different from zero and 64^3=8^x, then what is the value of
[#permalink]
24 May 2023, 05:44
24 May 2023, 05:44
Expert Reply
00:00
Question Stats:
100% (00:44) correct
0% (00:00) wrong based on 4 sessions
Hide Show timer Statistics
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
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
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
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
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If x is different from zero and 64^3=8^x, then what is the value of
[#permalink]
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
Moderators:
