Question

2^(log4^12)-3^(log9^27)+5^(log25^1/3)等于多少？

Answer 1

2^(log4^12)-3^(log9^27)+5^(log25^1/3)
=2^(log2(根号12))-3^(log3(根号27））+5^(log5(根号1/3)
=根号12-根号27+根号(1/3)
=2根号3-3根号3+1/3*根号3
=-2/3*根号3

Answer 2

log4^12
=lg12/lg4
=lg12/2lg2
=(1/2)lg12/lg2
=lg√12/lg2
=log2^√12
同理log9^27=log3^√27
log25^1/3=log5^(√1/3)

所以原式=2^(log2^√12)-3^(log3^√27)+5^[log5^(√1/3)]
=√12-√27+√(1/3)
=2√3-3√3+√3/3
=(-2/3)√3

Answer 3

2^(log4^12)-3^(log9^27)+5^(log25^1/3)
=[4^(log4^12)]^1/2-{9^(log9^27)}^1/2+[25^(log25^1/3)]^1/2
=√12-√27+√1/3
=2√3-3√3+√3/3
=-2√3/3