Evaluate the value of n where:
ln ( 1 ) + ln ( 2 ) + ln ( 3 ) + . . . + ln ( 1 2 ) = ln ( n )
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Since the sum of logarithms of numbers is equal to the logarithm of their product, the sum of the given logs = log(12!). Ed Gray
ln 1 + ln 2 + ln 3 + ⋯ + ln 1 2 = ln ( 1 × 2 × 3 × ⋯ × 1 2 ) = ln ( 1 2 ! ) ⟹ n = 1 2 ! = 4 7 9 0 0 1 6 0 0
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l n ( a ) + l n ( b ) = l n ( a ∗ b ) Therefore we can evaluate n as being 1 2 ∗ 1 1 ∗ 1 0 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 = 1 2 ! = 4 7 9 0 0 1 6 0 0 .