已知\;log_4m=log_6n=log_9(m+n)，\;試求\frac{n}{m}之值.

設：\;log_4m=log_6n=log_9(m+n)=k

則：\;m=4^k,\;n=6^k,\;m+n=9^k

⇒4^k+6^k=9^k...♠

又\;\frac{n}{m}=\left( \frac{6}{4}  \right)^k= \left( \frac{3}{2}  \right)^k

將♠式同除4^k得：\;1+\left( \frac{6}{4}  \right)^k=\left( \frac{9}{4}  \right)^k

⇒\left( \frac{9}{4}  \right)^k-\left( \frac{3}{2}  \right)^k-1=0

\frac{n}{m}=\frac{\sqrt5+1}{2}

$Step%v$

A: Corner[4] + (1, (-0.3))
n = 0 (slider from 0 to 10, step 1)
text7: "設\;t=\left( \frac{3}{2}  \right)^k>0" + (LaTeX[If[n ≥ 8, "⇒t^2-t-1=0"]]) + "" + (LaTeX[If[n ≥ 9, "⇒t=\frac{1±\sqrt5}{2}>0"]]) + ""