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imc

algebra intermediate

Problem

Suppose that

4^{a} = 5

,

5^{b} = 6

,

6^{c} = 7

, and

7^{d} = 8

. What is

a \cdot b \cdot c \cdot d

?

(A)

1

(B)

\frac{3}{2}

(C)

2

(D)

\frac{5}{2}

Solution

88888 2^{3} 3 a \cdot b \cdot c \cdot d = 7^{d} = (6^{c})^{d} = ((5^{b})^{c})^{d} = (((4^{a})^{b})^{c})^{d} = 4^{a \cdot b \cdot c \cdot d} = 2^{2 \cdot a \cdot b \cdot c \cdot d} = 2 \cdot a \cdot b \cdot c \cdot d = \frac{3}{2}

Final answer

B