Решение
1) Log_4 (10) + log_4 (1/640)=
log_4(10/640) = log_4 (1/64) = log_4 (4^(-3) )= - 3*log_4 (4) = - 3
Ответ: 2) – 3
2)
3log15 (<span>10) * 5log15 (10) = </span>(3*5)log15 (<span>10) = 15log15 (100 = 10</span>
Ответ: 2) 10
3) Log_3 (b⁻4) = 56, -4*log_3 b = 56, log_3 b = - 14
Log_3 b = - 14
Ответ: 1) -14
4)
m⁴ m³ logm(n)1/6 = m⁴ * m logm(n)1/2
= m⁴ *√n
Ответ: 4) = m⁴ *√n
5)
log23*log32
– log4(2)1/3 = 1 –(1/6) log22 = 1 – 1/6 = 5/6
Ответ: 3) 5/6
6)
log5 log2 log6 6³²
+ 10lg4 = log5 log2 32+ 4 = log5 log2
(2)⁵ + 4 = log5 5 + 4 = 1 + 4 = 5
Ответ: 5
7)
7log₇3 : log3 (1/3) + log336 –
2log32 = 3 : log₃(3⁻¹) + log₃ 4 +
log₃9 - 2log32 = - 1 + 2log33 + 2log32
- 2log32 = - 1 + 2 = 1
Ответ: 1
8)
Log345
/ log53 – log315 / log153 = (log33
+ log315)/ log53 – (log315*log315)/log53
=
= (1 + log3215) / log53 = (1 + log35)2 / log53
Ответ: (1 + log35)2 / log53
Решение
а) (2x + 7) + (-x + 12) = 14
2x + 7 - x + 12 = 14
x + 19 = 14
x = 14 - 19
x = - 5
б) (-5y + 1) - (3y + 2) = - 9
-5y + 1 - 3y - 2 = - 9
-8y - 1 = - 9
- 8y = - 9 + 1
-8y = -8
y = 1
(х² - 10х + 21)/(2х² - 15х + 7) = ((х - 3)(х - 7)) /((2х - 1)(х - 7)) = (х - 3)/(2х - 1)
А) -1,6; -1,5; 0; 3; 5,1; 6,5.
Б) 3; 5,1; 6,5.
В) -1,6; -1,5; -1.