Can someone answer. there is one question. there's a picture you!

The range of Cos(x) is [-1,1]. Therefore the range of ln(Cos(x)) will be the image of [-1,1] using the natural log function. However, the domain of ln(x) is (0,infinity) and the log function is strictly increasing with vertical asymptote at "x=0". Therefore, the range of ln(Cos(x)) will be: 

(- infinity, ln(1) ] = (-infinity, 0] !so its true