Question

Please solve for X and explain with steps

Answer 1

log₃(-2 tan(x)) = 1/2

Write both sides as powers of 3, and use the property $b^{\log_ba}=a$:

$3^{\log_3(-2\tan x)}=3^{\frac12}$

-2 tan(x) = √3

Then solve for x :

tan(x) = -√3 / 2

x = arctan(-√3 / 2) + nπ

x = -arctan(√3 / 2) + nπ

where n is any integer.