# Math Help - WOW. This is a tough extra credit logarithem!

1. ## WOW. This is a tough extra credit logarithem!

Find the value of this is the task:

[log base 2 (sin(11pi/6))^2]^3 + [log base 3 (tan(11pi/6))^2]^3

All I'm going to say is that this is seems very hard.

Forgive me if I am mistaken.

THANKS!

2. Originally Posted by Mr_Green
Find the value of this is the task:

[log base 2 (sin(11pi/6))^2]^3 + [log base 3 (tan(11pi/6))^2]^3

All I'm going to say is that this is seems very hard.

Forgive me if I am mistaken.

THANKS!
The first think you need to know is that $11 \pi /6$ is a special angle, and that:

$
\sin(11 \pi /6)=-1/2
$
and $
\ \ \ \tan(11 \pi /6)=-1/\sqrt{3}
$

so:

$
[\log_2 ((\sin(11\pi /6))^2)]^3 + [\log_3(\tan(11\pi /6))^2)]^3=$
$
[\log_2 (1/2^2)]^3 + [\log_3 (1/3)]^3
$

......= $=[-2]^3 + [-1]^3=-9$

RonL