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

Question

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}

lacktutor · Accepted Answer

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

—> 2^{3r—2s}= 2^{t}

3r—2s= t
r= \frac{( 2s+ t )}{3}

The answer is C.

Mohammadmo · Answer

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

Posted from my mobile device

fauji · Answer

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!

lorenz955 · Answer

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.

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

TheNightKing · Answer

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 ?

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

Prep Toolkit

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