Chain Reaction

Algebra Level 3

$\log _{ 2 }{ ((2+1)({ 2 }^{ 2 }+1)({ 2 }^{ 4 }+1)({ 2 }^{ 8 }+1)({ 2 }^{ 16 }+1)({ 2 }^{ 32 }+1)+1) } = ?$

1 solution

Tijmen Veltman
Apr 8, 2015

$\log_2((2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2^4-1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2^8-1)(2^8+1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2^{16}-1)(2^{16}+1)(2^{32}+1)+1)$

$=\log_2((2^{32}-1)(2^{32}+1)+1)$

$=\log_2(2^{64}-1+1)$

$=\boxed{64}.$

Isn't this question the same as this one ? :)

Nihar Mahajan - 6 years, 2 months ago

You put the same comment on both the answers xD

Omkar Kulkarni - 6 years, 2 months ago

Yeah you noticed it ... xD

Nihar Mahajan - 6 years, 2 months ago