Q5 of 50 Page 32

Find n is the equation 52 × 54 × 56 × … × 52n = (0.008)-30.

am× an = am + n


LHS = 52 × 54 × 56 × … × 52n


= 52 + 4 + 6 + …2n


= 52(1 + 2 + 3 + …n)


{1 + 2 + 3 + …n = }


=


= 5n(n + 1)


RHS = (0.008)-30 = (8× 10-3)-30


= (23× (2×5)-3)-30


= (23× 2-3× 5-3)-30


= 590


∵ (am)n = amn


LHS = RHS


∴ 5n(n + 1) = 590


∴ n(n + 1) = 90


∴n2 + n-90 = 0


Solving for n,


n = 9 and n = -10


But, n<0 is not possible


Hence, n = 9


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