已知\;a,b,c\;皆為正整數，\;且\;(a,b,c)=2014，\;若
\alog_{200}5+blog_{200}2=c，\;試求：\;a+b+c\;之值.

∵alog_{200}5+blog_{200}2=c

∴log_{200}5^a+log_{200}2^b=c

⇒log_{200}(5^a·2^b)=c

$Step%v$

又(a,b,c)=2014

A: Corner[4] + (0, (-0.5))
n = 0 (slider from 0 to 11, step 1)
text04: "⇒5^a·2^b=200^c" + (LaTeX[If[n ≥ 5, "=(2^3·5^2)^c"]]) + "" + (LaTeX[If[n ≥ 6, "=2^{3c}·5^{2c}"]]) + ""
text08: "⇒a=2c,b=3c" + (LaTeX[If[n ≥ 8, "⇒a:b:c=2:3:1"]]) + ""
text10: "所以a+b+c=2014×6" + (LaTeX[If[n ≟ 11, "=12084"]]) + ""