已知25的x次方=2000,80的y次方=2000,则x分之1+y分之1等于多少?
參考答案:已知25^x=2000，80^y=2000，求1/x+1/y=????
解：在已知的两边分别取常用对数，得
lg25^x=lg2000
xlg25=lg2000
x=lg2000/lg25
1/x=lg25/lg2000
lg80^y=lg2000
ylg80=lg2000
y=lg2000/lg80
1/y=lg80/lg2000
所以
1/x+1/y
=lg25/lg2000+lg80/lg2000
=(lg25+lg80)/lg2000
=lg(25*80)/lg2000
=lg2000/lg2000
=1
