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))
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：