3^a=5^b=A且1/a 1/b=2 求A

热心网友

3^a = 5^b = A且1/a + 1/b=2 求A.解:∵ a×log(A)3 = 1，b×log(A)5 = 1，故1/a = log(A)3，1/b = log(A)5即 log(A)3 + log(A)5 = 2log(A)15 = 2A^2 = 15∴A = √15

热心网友

3^a=A---a=log(3)A=lgA/lg3---1/a=lg3/lgA5^b=A---.................---1/b=lg5/lgA1/a+1/b=2---lg3/lgA+lg5/lgA=2---lg3+lg5=2lgA---1/2*lg(3*5)=lgA---lgA=lg√15---A=√15