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Answer :
Answer:
100
Step-by-step explanation:
Given 5·8^(n+1) = 625, you want the value of 4^(n+2).
Power of 2
We can rewrite each of these expressions as a power of 2:
[tex]8=2^3\\\\5\cdot 8^{(n+1)}=5\cdot(2^3)^{(n+1)}=5(2^{3n})(2^3)=40\cdot2^{3n}\\\\4=2^2\\\\4^{n+2}=(2^2)^{(n+2)}=(2^{2n})(2^4)=16\cdot2^{2n}[/tex]
Using the given value of the first expression, we find ...
[tex]40\cdot 2^{3n}=625\\\\2^{3n}=\dfrac{625}{40}=\dfrac{125}{8}=\left(\dfrac{5}{2}\right)^3\\\\\\2^{2n}=\left(\dfrac{5}{2}\right)^2=\dfrac{25}{4}\\\\\\4^{(n+2)}=16\cdot2^{2n}=16\cdot\left(\dfrac{25}{4}\right)=100\\\\\\\boxed{4^{(n+2)}=100}[/tex]
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Additional comment
n = (log(5)/log(2)) -1 ≈ 1.32192809489
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Rewritten by : Jeany
