一、已知X的对数,求X
1.loga x=1/2loga m+2loga n
loga x=logam^0.5+loga n ^2=loga n ^2*m^0.5
x=n^2(m)^0.5
2.loga x=2/3loga m-2loga n
loga x=loga m^(2/3)-loga n^2
x=m^(2/3)/ n^2
二、计算:
(1) 2^3+log2 5 = log2 2^3+log2 5=log2 40
(2)lg 5*lg 20+(lg 2)^2=lg 5(lg 2+1)+(lg 2)^2=lg 5+lg 2(lg 5+lg 2)=lg 5+lg 2=1
三、求下列各式中的X
(1) 3ln x-3=ln 2x
3ln x-3=ln 2+ln x
ln x=1/3(ln 2+3)
ln x=ln(2e^3)^1/3
x=e(2)^1/3
(2) lg x/10=-2-2lg x
lg x-1==-2-2lg x
3lg x=-1 lg x=lg10^(-1/3) x=10^(-1/3)
(3) log√ x(2X)=1/2
1/2 logx+ log2+ logx=1/2
3logx=1-log4
logx=log(5/2)^1/3
x=(5/2)^1/3