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4^5=4^20/4^x
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06 Sep 2019, 10:42
06 Sep 2019, 10:42
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Question Stats:
93% (00:22) correct
6% (00:26) wrong based on 45 sessions
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\(4^5=\frac{4^{20}}{4^x}\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
x |
4 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 4^5=4^20/4^x
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06 Sep 2019, 10:50
06 Sep 2019, 10:50
1
Carcass wrote:
\(4^5=\frac{4^{20}}{4^x}\)
Quantity A |
Quantity B |
x |
4 |
APPROACH 1: recognize that \(\frac{b^x}{b^y}=b^{x-y}\)
So, if \(\frac{4^{20}}{4^x}=4^5\), then we can rewrite it as \(4^{20-x}=4^5\), in which case, we can see that \(x = 15\)
Answer: A
---------------------------------
APPROACH 2:
GIVEN: \(4^5=\frac{4^{20}}{4^x}\)
Multiply both sides by \(4^x\) to get: \((4^5)(4^x)=4^{20}\)
Simplify left side to get: \(4^{5+x}=4^{20}\)
This means: \(5+x = 20\), which means \(x=15\)
---------------------------------
Answer: A
Cheers,
Brent
Re: 4^5=4^20/4^x
[#permalink]
06 Sep 2019, 20:29
06 Sep 2019, 20:29
1
GIVEN: 45=4204x45=4204x
Multiply both sides by 4x4x to get: (45)(4x)=420(45)(4x)=420
Simplify left side to get: 45+x=42045+x=420
This means: 5+x=205+x=20, which means x=15
Multiply both sides by 4x4x to get: (45)(4x)=420(45)(4x)=420
Simplify left side to get: 45+x=42045+x=420
This means: 5+x=205+x=20, which means x=15
