SOLUTION: What is the degree - measure of the least positive angle x such that {{{ log 2 (cosx)=-1/2 }}} (base 2).

Algebra ->  Trigonometry-basics -> SOLUTION: What is the degree - measure of the least positive angle x such that {{{ log 2 (cosx)=-1/2 }}} (base 2).      Log On


   

Question 1110426: What is the degree - measure of the least positive angle x such that +log+2+%28cosx%29=-1%2F2+ (base 2).
Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
log%282%2C%28cos%28x%29%29%29 = -1%2F2   <==== is equivalent to  ====>


cos(x) = 2%5E%28-0.5%29 = 1%2Fsqrt%282%29 = sqrt%282%29%2F2   <=== ===>


x = pi%2F4.


Answer.   The least positive angle x such that  log%282%2C%28cos%28x%29%29%29 = -1%2F2   is  x = pi%2F4,  or  45 degrees.