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Algebra Level 2

Evaluate the value of n n where:

ln ( 1 ) + ln ( 2 ) + ln ( 3 ) + . . . + ln ( 12 ) = ln ( n ) \ln(1)+\ln(2)+\ln(3)+...+\ln(12) = \ln(n)


The answer is 479001600.

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3 solutions

l n ( a ) + l n ( b ) = l n ( a b ) ln(a) + ln(b) = ln(a*b) Therefore we can evaluate n n as being 12 11 10 9 8 7 6 5 4 3 2 1 = 12 ! = 479001600 12*11*10*9*8*7*6*5*4*3*2*1 =12! =479001600 .

Edwin Gray
Aug 25, 2018

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

Chew-Seong Cheong
Mar 24, 2018

ln 1 + ln 2 + ln 3 + + ln 12 = ln ( 1 × 2 × 3 × × 12 ) = ln ( 12 ! ) \ln 1 + \ln 2 + \ln 3 + \cdots + \ln 12 = \ln (1\times 2 \times 3 \times \cdots \times 12) = \ln(12!) n = 12 ! = 479001600 \implies n = 12! = \boxed{479001600}

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