Fair value and carrying value (historical value-based measurement) are the two primary accounting measurements. According to GAAP, many investments use fair value as the measurement basis, but intangible asset uses carrying value. This measurement difference is significant between investment accounting and intangible asset accounting. Demonstrate why GAAP chooses fair value to measure investment, but it only permits the use of historic-based carrying value to measure intangible assets.

Write up an easy more than 500 words to illustrate the difference. The solution needs to provide the following information (but not limited to):

(1) the definition and the primary features of these two measurements;

(2) the precondition that we can use fair value as a robust accounting measurement;

(3) some specific conditions that we need to avoid using fair value.