Find the exact value of ... ln(log4 4^e^2)

Question

In case it ain't clear in the top...

Find the exact value of:

 

ln (log₄ 4^{e^2})

Answer 1

ln(log₄ 4^{e^2}) = ln(e² log₄4) = ln(e² * 1) = ln(e²) = 2 ln(e) = 2*1 = 2