数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 04:19:50
![数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))](/uploads/image/z/2483985-57-5.jpg?t=%E6%95%B0%E5%AD%A6%28log5+%E2%88%9A2%2Alog7+9%29%2F%28log5+1%2F3+%2Alog7+3%E2%88%9A4%29%2Blog2%28+%E2%88%9A%283%2B%E2%88%9A5%29-+log%E2%88%9A%283-%E2%88%9A5%29%29)
数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))
数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))
数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))
数学(log5 √2*log7 9)/(log5 1/3 *log7 3√4)+log2( √(3+√5)- log√(3-√5))
=(lg√2/lg5 *lg9/lg7)/(lg1/3/lg5 *lg3√4/lg7)+log2( √( 3+√5)/√(3-√5))
=(1/2lg2/lg5 *2lg3/lg7)/(-lg3/lg5 *2/3lg2/lg7)+log2( ( 3+√5)/√(9-5))
=(lg2*lg3)/(lg5*lg7) /(-2/3*lg2*lg3/(lg5*lg7))+log2( ( 3+√5)/2)
=(lg2*lg3)/(lg5*lg7) *(-3/2*lg5*lg7/(lg2*lg3))+log2( ( 3+√5)/2)
=-3/2+lg ( 3+√5) -1
=-5/2+lg ( 3+√5)
见图: