1. 次の対数の値を求めよ。
1 4
( ) log2 ( ) log32 1
27 3
( ) log2 2 ( ) log44 1
5 2 ( ) log
2 ( ) log2 86
7 2
( ) log8 ( ) log0.58 4
9 ( ) log9 1
3
2. 次の式を簡単にせよ。
1 3+ 9
( ) log2 log2 ( ) log3 log32 4- 64
3 6+ 12
( ) log2 log2 ( )3 2log2450-4log260
5 + ( ) log33
5 log35
3 ( ) log2 126 -1 27
6log2
3. 次の式を簡単にせよ。
1 3- 9
( ) log2 log4 ( ) log9 log272 6+ 6
3 5- 5 ( ) log4 log 2
4. 次の式を簡単にせよ。
1 3⋅ 2
( ) log2 log3 ( ) log3 log32 8÷ 16
3 ( 3+ 9 ( 8+ 16 ( ) log2 log4 ) log3 log9 )
5. 次の式の値を求めよ。
1 3
( ) log32 ( )2 21+log25
6. a =log23, b =log25 とするとき、次の式を a, b で表せ。
1 45
( ) log2 ( ) log22 20
3 75
( ) log4 ( ) log2 154
7. a =log210, b =log36 とするとき、次の式を a, b で表せ。
1 5+ 2
( ) log2 log3 ( ) log3 log22 10⋅ 6
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ちゃんと理解したい⼈のための⾼校数学
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1. 次の対数の値を求めよ。
1 4 = 2 = 2 2 = 2 ( ) log2 log2 2
log2 ( ) log32 1= 3 = -3 3 = -3
27 log3 -3
log3
3 = 2 = 2 =
( ) log2 2 log2 1 2 1
2log2 1 2
4 1 = 0 ( ) log4 5 2
( ) log 2
=log ( ) = 2 = 2 2 2 2 log
2 2
6 ( ) log2 8
=log28 = (2 ) = 2 = 1 1
3 log2 3 1 3 log2
7 2 = = = =
( ) log8 2 8 log2 log2
2 2 log2 log2 3
2
3 2
log2 log2
1 3
8 4 ( ) log0.5 =
4 0.5 log2 log2
=log24= = = -2
log21 2
2 2 log2 2 log2 -1
2 2
- 2
log2 log2 9
( ) log9 1 3
=log9 1 = 3 = - 3 3
1 2
log9 -1
2 1
2log9 = -1 = - = -
2 3 9 log3 log3
1 2
3 3 log3 log3 2
1 4
2. 次の式を簡単にせよ。
1 3+ 9 ( ) log2 log2 =log2( )3⋅9
=log227 =log23 = 33 3 log2
2 4- 64 ( ) log3 log3 = log34
64
=log31= 2 = -4 2 16 log3 -4
log3 3 6+ 12
( ) log2 log2 =log2(6⋅12) =log272 =log2(2 ⋅33 2)
=log22 +3 log23 = 3+22 3 log2
3 2 450-4 60 ( ) log2 log2 =log2450 -2 log2604 = log2(2⋅3 ⋅5
(2 ⋅3⋅5 2 2)2 2 )4 =log21 = 2 = -6
26 log2 -6 5 +
( ) log33 5 log35
3 =log3 3⋅
5 5 =log31 = 03
6 - 27
( ) log2 12 1 6log2 =log2 )(12 - (3
1
2 log2 3) 1 6
=log2 )(12 - 3 1 2 log2
1 2
=log212 = 4 = 2 = 1 3
1 2
log2 1 2 log2
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ちゃんと理解したい⼈のための⾼校数学
@YouTube3
3. 次の式を簡単にせよ。
1 3- 9 ( ) log2 log4 =log23- 3
2 log2 2 log2 2 =log23-2 3= 0
2 log2
2 6+ 6 ( ) log9 log27
= -
6 3 log3 log3 2
6 3 log3 log3 3
=1 6- 6 = 6
2log3 1 3log3 1
6log3 3 5- 5
( ) log4 log 2
= -
5 2 log2 log2 2
5
2 log2 log2
1 2
=1 5-2 5 = - 5 2log2 log2 3
2log2
4. 次の式を簡単にせよ。
1 3⋅ 2 ( ) log2 log3
= log23⋅ = 2 = 1 2
3 log2 log2 log2
2 8÷ 16 ( ) log3 log3 =log32 ÷3 log324 = 3log32÷4log32 =3
4 3 ( 3+ 9 ( 8+ 16
( ) log2 log4 ) log3 log9 )
= log23+ 2 +
3 2 log2 2
log2 2 log3 3 2 3 log3 4 log3 2 =(log2 log2 )( log33+ 3 3 2+2log3 )2 = 2log2 log33⋅5 2
= 10
5. 次の式の値を求めよ。
1 3 = A ( ) log32
log33log32= A log3 log32 = Alog3 A = 2 ∴ 3log32= 2
2 2 = 2⋅2 ( ) 1+log25 log25 2log25= A log22log25= A
log2 log2 log25 = A A = 5
∴ 21+log25= 2⋅5 = 10
6. a =log23, b =log25 とするとき、次の式を a, b で表せ。
1 45 ( ) log2 =log2(3 ⋅52 ) =log23 +2 log25 = 2log2 log23+ 5 = 2a+b
2 20 ( ) log2 =log2(2 ⋅52 ) =log22 +2 log25 = 2+log25 = 2+b 3 75
( ) log4 =
(3⋅5 2 log2 2)
log2 2 = (1 3+ 5
2log2 log2 2) = (1 3+2 5 = a+2b
2log2 log2 ) 1 2( )
4 ( ) log2 15 =log215
1 2 =1 3⋅5
2log2( ) =1 3+ 5
2(log2 log2 ) = a+b1
2( )
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ちゃんと理解したい⼈のための⾼校数学
@YouTube7. a =log210, b =log36 とするとき、次の式を a, b で表せ。
1 5+ 2 ( ) log2 log3 =log210+
2 log36
=log2 log2 log3 log310- 2+3 6- 3 = a+b-2 ＊別解
a =log210 =log22⋅5 = 1+log25, よって log25 = a-1 b =log3 log36 = 3⋅2 = 1+log32, よって log36 = b-1 log2 log35+ 2 = a+b-2
2 10⋅ 6 ( ) log3 log2 = 10⋅
3 log2
log2 6 2 log3 =log2 log310⋅ log36 = ab
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