作业帮高一两题对数计算题求解答
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高一两题对数计算题求解答
两题在这里,给个思路也可以
两题在这里,给个思路也可以
[ (1-log6【3】)^2 + log6【2】* log6【18】] ÷log6【4】
= [ (log6【6】-log6【3】)^2 + log6【2】* log6【2*9】] ÷log6【2^2】
= [ (log6【6/3】)^2 + log6【2】* log6【18】] ÷ [2log6【2】]
= [ (log6【2】) + log6【18】] ÷ 2
= [ (log6【2*18】] ÷ 2
= [ (log6【6^2】] ÷ 2
= 2 ÷ 2
= 1
( log2【5】+ log4【125】)* log3【2】/ log√3【5】
= ( lg5 / lg2+ lg125 / lg4) * (lg2 / lg3)/ ( lg5 / lg√3)
= ( lg5 / lg2+ lg5^3 / lg2^2) * (lg2 / lg3)/ ( lg5 / lg√3)
= [ lg5 / lg2+ 3 lg5 / (2lg2)] * (lg2 / lg3)/ [lg5 / (1/2 lg3)]
= [2 lg5 + 3 lg5 / (2 lg2)] * (lg2 /(2 lg5)
= [5 lg5 / (2 lg2)] * (lg2 /(2 lg5)
= 5/2 * 1/2
= 5/4
= [ (log6【6】-log6【3】)^2 + log6【2】* log6【2*9】] ÷log6【2^2】
= [ (log6【6/3】)^2 + log6【2】* log6【18】] ÷ [2log6【2】]
= [ (log6【2】) + log6【18】] ÷ 2
= [ (log6【2*18】] ÷ 2
= [ (log6【6^2】] ÷ 2
= 2 ÷ 2
= 1
( log2【5】+ log4【125】)* log3【2】/ log√3【5】
= ( lg5 / lg2+ lg125 / lg4) * (lg2 / lg3)/ ( lg5 / lg√3)
= ( lg5 / lg2+ lg5^3 / lg2^2) * (lg2 / lg3)/ ( lg5 / lg√3)
= [ lg5 / lg2+ 3 lg5 / (2lg2)] * (lg2 / lg3)/ [lg5 / (1/2 lg3)]
= [2 lg5 + 3 lg5 / (2 lg2)] * (lg2 /(2 lg5)
= [5 lg5 / (2 lg2)] * (lg2 /(2 lg5)
= 5/2 * 1/2
= 5/4