If 8^r/4^s =2^t, then what is r in terms of s and t ? (2024)

If 8^r/4^s =2^t, then what is r in terms of s and t ? (1)

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Bunuel

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If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]24 Oct 2019, 02:14

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If 8^r/4^s =2^t, then what is r in terms of s and t ? (15)

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If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)

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If 8^r/4^s =2^t, then what is r in terms of s and t ? (22)

D

lacktutor

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If 8^r/4^s =2^t, then what is r in terms of s and t ? (23)

Joined: 25 Jul 2018

Posts: 667

If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]24 Oct 2019, 02:45

Mohammadmo wrote:

2^3r /2^2s=2^t
3r/2s=t
r=2st/3
Option D

Posted from my mobile device

\(\frac{2^{3r}}{2^{2s}}= 2^{t}\)

—>\(2^{3r—2s}= 2^{t}\)

3r—2s= t
r=\(\frac{( 2s+ t )}{3}\)

The answer is C.

If 8^r/4^s =2^t, then what is r in terms of s and t ? (25)

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Mohammadmo

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If 8^r/4^s =2^t, then what is r in terms of s and t ? (26)

Joined: 29 Jun 2019

Posts: 358

Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]24 Oct 2019, 02:29

2^3r /2^2s=2^t
3r/2s=t
r=2st/3
Option D

Posted from my mobile device
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If 8^r/4^s =2^t, then what is r in terms of s and t ? (28)

D

fauji

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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]24 Oct 2019, 03:41

Approach:

Simplify the given equation:

\(\frac{8^r}{4^s} =2^t --> 2^3 ^r=2^t*2^2 ^s\)

\(3r = t + 2s\)

\(r = \frac{2s+t}{3}\)

IMO Option C it is!

If 8^r/4^s =2^t, then what is r in terms of s and t ? (31)

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lorenz955

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If 8^r/4^s =2^t, then what is r in terms of s and t ? (32)

Joined: 07 Jan 2019

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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]24 Oct 2019, 09:04

Q: 8^r/4^s=2^t

8^r=2^3r and 4^s=2^2s

so we have: 2^3r/2^2s=2^t

for the rules of the exponents--->x^y/x^z=x^(y-z) this means 2^3r/2^2s=2^(3r-2s)

2^(3r-2s)=2^t---->3r-2s=t---->r=(t+2s)/3

hope this helps.

If 8^r/4^s =2^t, then what is r in terms of s and t ? (34)

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ScottTargetTestPrep

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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]29 Oct 2019, 07:24

Expert Reply

Bunuel wrote:

If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)

Simplifying the equation, we have:

2^(3r)/2^(2s) = 2^t

2^(3r-2s) = 2^t

3r - 2s = t

3r = 2s + t

r = (2s + t)/3

Answer: C
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If 8^r/4^s =2^t, then what is r in terms of s and t ? (37)

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Kinshook

GMAT Club Legend

If 8^r/4^s =2^t, then what is r in terms of s and t ? (38)

Joined: 03 Jun 2019

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Location: India

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GMAT 1: 690 Q50 V34 If 8^r/4^s =2^t, then what is r in terms of s and t ? (39)

WE:Engineering (Transportation)

Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]29 Oct 2019, 07:50

Bunuel wrote:

If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)

If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

\(2^{3r-2s} = 2^t\)
3r -2s = t
\(r = \frac{2s + t}{3}\)

IMO C

If 8^r/4^s =2^t, then what is r in terms of s and t ? (42)

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TheNightKing

VP

If 8^r/4^s =2^t, then what is r in terms of s and t ? (43)

Joined: 18 Dec 2017

Posts: 1169

Location: United States (KS)

GMAT 1: 600 Q46 V27 If 8^r/4^s =2^t, then what is r in terms of s and t ? (44)

Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]14 Nov 2019, 19:00

Bunuel wrote:

If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)

Just take 8/4=2 which makes r=s=t=1

Only Option C works.

If 8^r/4^s =2^t, then what is r in terms of s and t ? (46)

gmatclubot

Re: If 8^r/4^s =2^t, then what is r in terms of s and t ?[#permalink]

14 Nov 2019, 19:00

If 8^r/4^s =2^t, then what is r in terms of s and t ? (2024)

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