Поэтажное и поэтапное решение примеров на упрощение логарифмических выражений (ЕГЭ-2009)







































9log345 = 32log345 = 3log3452 = 452 = 45

3log945 = 3log3245 =
31
-
2		 log345
 =
3log345 1
-
2
 =
45 1
-
2
 =
√ —
45
 =
3√ –
5

3log 1
-
9		 45
 = 3log3-245 =
3 - 1
-
2		 log345
 =
3log345 - 1
-
2
 =
45 - 1
-
2
 =
1
—
√45
=
1
–
3√5

√ —
3
 log945 =
31
-
2		 log3245
 =
32
-
2		 log345
 =
3log345 1
-
2
 =
45 1
-
2
 =
√ —
45
 =
3√ –
5

√ —
3
log 1
-
9		 45
 =
31
-
2		 log3-245
 =
3 - 2
-
2		 log345
 =
3log345 - 2
-
2
 =
45 - 2
-
2
 =
1
—
√45
=
1
–
3√5

3log√545 = 3log30,545 = 32log345 = 3log3452 = 452 = 45

log√5125 = log50,553 = 2·3log55 = 6



log√5√6 = log50,560,5 = log56

2 log5√6 = log5√62 = log56

2 log37 — 3 log35 = log372 — log353 = log349 — log3125 =
log3 49
—
125

2 log37 + 3 log35 = log372 + log353 = log349 + log3125 =
log3 (49·125)

log5log232 = log55 = 1

log6log5log232 = log6log55 = log61 = 0

1
-
2		 log67 = log6√7 = log62√2