Suppose 4a = 5, 5b = 6, 6c = 7, 7d = 8, then the value of abcd is = ?
A. 1
B. $$\frac{3}{2}$$
C. 2
D. $$\frac{5}{2}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & 8 = {7^d} \cr & \,\,\,\,\,\, = {\left( {{6^c}} \right)^d} \cr & \,\,\,\,\,\, = {\left( {{5^b}} \right)^{cd}} \cr & \,\,\,\,\,\, = {5^{bcd}} \cr & \,\,\,\,\,\, = {\left( {{4^a}} \right)^{bcd}} \cr & \,\,\,\,\,\, = {4^{abcd}} \cr & \Rightarrow {4^{abcd}} = 8 \cr & \Rightarrow {\left( {{2^2}} \right)^{abcd}} = {2^3} \cr & \Rightarrow 2abcd = 3 \cr & \Rightarrow abcd = \frac{3}{2} \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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