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If , then what is r in terms of s and t ?
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28 Oct 2018, 17:48
28 Oct 2018, 17:48
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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. \(\frac{s}{2}+\frac{t}{4}\)
A. \(s + t + 1\)
B. \(s + t + 5\)
C. \(\frac{2s+t}{3}\)
D. \(\frac{2st}{3}\)
E. \(\frac{s}{2}+\frac{t}{4}\)
Re: If , then what is r in terms of s and t ?
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25 Dec 2018, 12:42
25 Dec 2018, 12:42
sandy 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. \(\frac{s}{2}+\frac{t}{4}\)
A. \(s + t + 1\)
B. \(s + t + 5\)
C. \(\frac{2s+t}{3}\)
D. \(\frac{2st}{3}\)
E. \(\frac{s}{2}+\frac{t}{4}\)
\(\frac{2^3^s}{2^2^s}=2^t\)
=>\(2^3^r^-^2^s=2^t\)
=>3r-2s=t
=>3r=2s+t
=>r=\(\frac{2s+t}{3}\)
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Re: If , then what is r in terms of s and t ?
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20 Sep 2022, 09:03
20 Sep 2022, 09:03
1
Given that \(\frac{8^r}{4^s}=2^t\) and we need to find what is r in terms of s and t
\(\frac{8^r}{4^s}=2^t\) => \(\frac{(2^3)^r}{(2^2)^s}=2^t\)
=> \(\frac{2^{3*r}}{2^{2*s}}=2^t\) => \(2^{3r - 2s}=2^t\)
Since base is same (2) on both the sides => power will also be the same
=> 3r - 2s = t
=> 3r = t + 2s
=> r = \(\frac{t + 2s}{3}\)
So, Answer will be C
Hope it helps!
\(\frac{8^r}{4^s}=2^t\) => \(\frac{(2^3)^r}{(2^2)^s}=2^t\)
=> \(\frac{2^{3*r}}{2^{2*s}}=2^t\) => \(2^{3r - 2s}=2^t\)
Since base is same (2) on both the sides => power will also be the same
=> 3r - 2s = t
=> 3r = t + 2s
=> r = \(\frac{t + 2s}{3}\)
So, Answer will be C
Hope it helps!
