1. The exponent (that is cos x) is never larger than 1 ....

2. Assuming base 10, you have and it should be clear that .... By the way, a number thetadoesexist (in fact, an infinite number of values exist) but it's not real. The question should be worded as "Explain why there does not exist arealnumber theta such that: log cos(theta) = 0.1".