关于log的计算log8（9）*log27(32)log4(3)*log9（2）-log1/2（四倍根号下32）[log2(5)+log4(0.2)][log5(2)+log25(0.5)]小括号里的数字是真数,小括号外的数字是底数

Question

关于log的计算
log8（9）* log27 (32)
log4 (3) *log9（2）- log 1/2（四倍根号下32）
[log2(5)+log4(0.2)][log5(2)+log25(0.5)]
小括号里的数字是真数,小括号外的数字是底数

Answer 1

log8（9）× log27 (32)
= (2/3)log2 (3) ×(5/3)log3(2)
= (2/3)×(5/3)
= 10/9
log4 (3) ×log9（2）- log 1/2（4√32）
=(1/2)log2(3) ×(1/2)log3(2) + log2(16√2)
= 1/4 + 9/2
= 19/4
[log2(5)+log4(0.2)][log5(2)+log25(0.5)]
=[log2(5) - (1/2)log2(5)][log5(2) - (1/2)log5(2)]
= (1/2)log2(5)×(1/2)log5(2)
= 1/4