Question

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

• A. $1$
• B. $\frac{3}{2}$
• C. $2$
• D. $\frac{5}{2}$

Answer 1

Answer: (B)

$\frac{3}{2}$

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