Question

| log(0.5)tan[PI/3] | / log(0.5)tan[PI/3]
Log bases are in ( )

Answer 1

1?

Answer 2

\[\LARGE \frac{\log_{0.5}\tan \cfrac{\pi}{3} }{\log_{0.5}\tan\cfrac{\pi}{3}}\] ?? LOL

Answer 3

Upper one is an absolute value

Answer 4

\[\frac{| log_{(0.5)}tan[\pi/3] |} { log_{(0.5)}tan[\pi/3]} \]
\[tan \pi/3= \sqrt 3\]
One point to note that
0.5 is less than 1 so
0.5 has to be raised to a negative power to get \(\sqrt 3\)
so
we have
\[\frac{|negative|}{negative}\]
\[\huge \frac{positive}{negative}=-1\]

Answer 5

Thank you! I have two more of them, I'll put them to the left.