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

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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] New post   24 Oct 2019, 02:14
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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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lacktutor
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If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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.
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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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!
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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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.
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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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
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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink] New post   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.
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Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
14 Nov 2019, 19:00
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