Suppose 4a=5, 5b=6, 6c=7, 7d=8, then the value of abcd is (A.A.O. Exam, 2009) · ABC26GN1980
Subject: General Aptitude · Chapter: Surds and Indices
Suppose $4^{a}=5, 5^{b}=6, 6^{c}=7, 7^{d}=8$, then the value of $abcd$ is (A.A.O. Exam, 2009)
(a)1
(b)$\frac{3}{2}$
(c)2
(d)$\frac{5}{2}$
Answer
Explanation
$$8=7^{d}=\left(6^{c}\right)^{d}=6^{cd}=\left(5^{b}\right)^{cd}=5^{bcd}=\left(4^{a}\right)^{bcd}=4^{abcd}$$ $$\Rightarrow 4^{abcd}=8 \Rightarrow \left(2^{2}\right)^{abcd}=2^{3} \Rightarrow 2abcd=3 \Rightarrow abcd=\frac{3}{2}.$$
Explanation as extracted from the printed page; notation may be imperfect.
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