log3 2(log 4 3+log8 3)怎么做 2,3在上面

log3 2(log 4 3+log8 3)怎么做 2,3在上面
log3 2(log 4 3+log8 3)怎么做 2,3在上面

log3 2(log 4 3+log8 3)怎么做 2,3在上面
换底公式
原式=(lg2/lg3)(lg3/lg4+lg3/lg8)
=(lg2/lg3)(lg3/2lg2+lg3/3lg2)
=(lg2/lg3)(lg3/2lg2)+(lg2/lg3)(lg3/3lg2)
=1/2+1/3
=5/6

log3 2(log 4 3+log8 3)
=log3 2(log 2^2 3+log2^3 3)
=log3 2(log 2 3^(1/2)+log2 3^(1/3))
=log3 2(log 2 3^(1/2)+log2 3^(1/3))
=log3 2*(1/2+1/3)log 2 3
=5/6*log3 2*log2 3
=5/6.