PC用は別頁
※高校数学Ⅱの「指数関数」について,このサイトには次の教材があります.
この頁へGoogleやYAHOO ! などの検索から直接来てしまったので「前提となっている内容が分からない」という場合や「この頁は分かったがもっと応用問題を見たい」という場合は,他の頁を見てください.  が現在地です.
負の指数
同(2)
指数法則
同(2)
理科における有効数字の表し方
累乗根
同(2)
分数の指数
同(2)
ax+a−xの値
指数関数のグラフ
指数と大小比較
n乗比較
指数方程式
同(2)
指数不等式
指数が対数のもの


== 指数方程式の解き方 ==
[要点]
1 ax=ay の形にできれば x=y です。(a≠1)
2 ax=b の形ならば x=logab <・・・対数を習ってから
3 ax=t (>0)とおくと,tの方程式にできるものがあります。

●1の解説:
 次のグラフは,関数 y=ax を表わしたものです。

a>1,0<a<1のいずれの場合においても
p≠qならばa≠a
です。だから,(対偶により)
=aならばp=q
です。
 (指数関数が等しい → 指数が等しい)
1の例
 22x-4=22-x → 2x-4=2-x 
 これで指数は外れましたので、あとは単なる1次方程式です。
 3x=6 より x=2・・・答

●2の解説:
 「指数形式の書き方」と「対数形式の書き方」の読みかえ方の約束です。
  例 2=8 と書くことを対数の形式では 3=log8 と書きます。
  例 log10100=2 とは 102=100 のことです。

2の例
 2=3 →(右辺が2の形にならない)→ x=log23・・・答

●3の解説:
 ax=t とおくと簡単に解けることがあります。この置き換えを用いる場合,右のグラフのようにaxが正の値だけを取ることに注意することが大切です。

ax=t とおくと t>0 です!!。(xはマイナスでも可)

3の例
 4x-2x-2=0 → 2x=t (ただしt>0) とおくとt2-t-2=0
 → (t-2)(t+1)=0 → t=2,-1 ここでt>0だからt=2
 → 2x=2 より x=1 ・・・答


■問題・・・次の方程式を解きなさい。
93x=27x-1
x=
[ヒント]

x=
[ヒント]

x=
[ヒント]

x=
[ヒント]


--※対数を習ってからする問題
=5
(解答を1つ選びなさい。)
x=log35, x=log53, x=-log35, x=-log53
[ヒント]
--※対数を習ってからする問題 
2=3-x
(解答を1つ選びなさい。)
x=log23, x=log32, x=-log23, x=-log32
[ヒント]
9x-4・3x+3=0
(解答を1つ選びなさい。)
x=1, x=0,1, x=3, x=1,3
[ヒント]
22x-2x+1-8=0
x=
[ヒント]

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■[個別の頁からの質問に対する回答][指数方程式について/16.10.22]
最後の問題8番の、2の2x乗-2のx+1乗-8についての質問です。ヒントでは2のx乗をtとすると、tの2乗-2t-8になるとあります。しかし、tの2乗+4t-8になるような気がして、そこで行き詰ってしまったのですが、いかがでしょうか。
=>[作者]:連絡ありがとう.あなたの場合は,指数法則が十分身に付いていないという弱点があるようですので,この頁で復習するとよいでしょう.なお,指数法則や対数の計算規則は,1つの問題の中で何回も多重的に登場しますので,(水や空気に親しむように)反復練習が必要です.
元の問題:
amn=(am)nだから2x=tとおくと22x=(2x)2=t2
次に
am+n=amanだから2x+1=2x21すなわち2x+1=2t
になります.
−2x+1(−2)22x→4tにはなりません

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