已知27²=a^6=9^b,求2a²+2ab的值.已知:5^a=4,5^b=6,5^c=9 试说明2b=a+c

问题描述:

已知27²=a^6=9^b,求2a²+2ab的值.已知:5^a=4,5^b=6,5^c=9 试说明2b=a+c

27²=(3³)²=3^69^b=3^(2b)a=3,b=32a²+2ab=2×3²+2×3×3=365^a=4,5^b=6,5^c=9 a=log5 4 ,b=log5 6 ,c=log5 92b=2log5 6=log5 36a+c=log5 4+log5 9=log5(4×9)=log5 36所以,2b=a+c