Question

若3^x=4^y=36，則=________．

Answer 1

1
分析：由指數(shù)式和對(duì)數(shù)式的關(guān)系可得x=log₃³⁶，y=log₄³⁶，∴+=2×log₃₆³+log₃₆⁴，再利用對(duì)數(shù)的運(yùn)算
性質(zhì)化簡(jiǎn)求值．
解答：∵3^x=4^y=36，
∴x=log₃³⁶，y=log₄³⁶，
∴+=2×log₃₆³+log₃₆⁴=log₃₆⁹+log₃₆⁴=log₃₆³⁶=1，
故答案為 1．
點(diǎn)評(píng)：本題考查指數(shù)式和對(duì)數(shù)式的互化，對(duì)數(shù)的運(yùn)算性質(zhì)的應(yīng)用，換底公式的應(yīng)用．