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Suppose 4^a = 5, 5^b = 6, 6^c = 7, 7^d = 8, then the value of abcd is = ?

11
2³/₂
32
4⁵/₂

Answer:- 1

Explanation:-

Solution:

\begin{aligned} 8 = 7^{d} \\ = {(6^{c})}^{d} \\ = {(5^{b})}^{c d} \\ = 5^{b c d} \\ = {(4^{a})}^{b c d} \\ = 4^{a b c d} \\ \Rightarrow 4^{a b c d} = 8 \\ \Rightarrow {(2^{2})}^{a b c d} = 2^{3} \\ \Rightarrow 2 a b c d = 3 \\ \Rightarrow a b c d = \frac{3}{2} \end{aligned}

$\eqalign{ & 8 = {7^d} \cr & \,\,\,\,\,\, = {\left( {{6^c}} \right)^d} \cr & \,\,\,\,\,\, = {\left( {{5^b}} \right)^{cd}} \cr & \,\,\,\,\,\, = {5^{bcd}} \cr & \,\,\,\,\,\, = {\left( {{4^a}} \right)^{bcd}} \cr & \,\,\,\,\,\, = {4^{abcd}} \cr & \Rightarrow {4^{abcd}} = 8 \cr & \Rightarrow {\left( {{2^2}} \right)^{abcd}} = {2^3} \cr & \Rightarrow 2abcd = 3 \cr & \Rightarrow abcd = \frac{3}{2} \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} 8 = 7^{d} \\ = {(6^{c})}^{d} \\ = {(5^{b})}^{c d} \\ = 5^{b c d} \\ = {(4^{a})}^{b c d} \\ = 4^{a b c d} \\ \Rightarrow 4^{a b c d} = 8 \\ \Rightarrow {(2^{2})}^{a b c d} = 2^{3} \\ \Rightarrow 2 a b c d = 3 \\ \Rightarrow a b c d = \frac{3}{2} \end{aligned}

$\eqalign{ & 8 = {7^d} \cr & \,\,\,\,\,\, = {\left( {{6^c}} \right)^d} \cr & \,\,\,\,\,\, = {\left( {{5^b}} \right)^{cd}} \cr & \,\,\,\,\,\, = {5^{bcd}} \cr & \,\,\,\,\,\, = {\left( {{4^a}} \right)^{bcd}} \cr & \,\,\,\,\,\, = {4^{abcd}} \cr & \Rightarrow {4^{abcd}} = 8 \cr & \Rightarrow {\left( {{2^2}} \right)^{abcd}} = {2^3} \cr & \Rightarrow 2abcd = 3 \cr & \Rightarrow abcd = \frac{3}{2} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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