Logs and Logs

Algebra Level 2

Compute:

$(\log_2(3))\times(\log_3(4))\times(\log_4(5))\times\cdots\times(\log_{63}(64))=?$

8 10 2 4 6

1 solution

Hana Wehbi
Mar 11, 2017

$(\log_2(3))\times(\log_3(4))\times(\log_4(5))\times\cdots\times(\log_{63}(64))=$

$\large\frac{\ln(3)}{\ln(2)}\times\frac{\ln(4)}{\ln(3)}\times\frac{\ln(5)}{\ln(4)}\times...\times\frac{\ln(64)}{\large\ln(63)}$ = $\large\frac{\ln(64)}{\ln(2)}=\frac{6\ln(2)}{\ln(2)}=6$

@Hana Nakkache What is In? Is there any wiki for this ?

Toshit Jain - 4 years, 3 months ago

Natural Log or Log base e.

Hana Wehbi - 4 years, 3 months ago

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