Q. 54.5( 2 Votes )
Find n is the equation 52 × 54 × 56 × … × 52n = (0.008)-30.
Answer :
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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