1. log₃(x+5)=2. x+5>0, x>-5
x+5=3², x+5=9
<u>x=4</u>
2. log₁/₅(2x+7)=-2. 2x+7>0, x>-3,5
2x+7=(1/5)⁻²
2x+7=25
<u>x=9</u>
3. log₆(x²+8)=log₆(6x-1)
{x²+8>0
6x-1>0, x>1/6
x²+8=6x-1
x²-6x+9=0, (x-3)²=0
<u>x=3</u>
4. log₃x+2log_x 27 -=0
log₃x+2*(log₃27/log₃x)-5=0
log₃x+6/log₃x-5=0
log₃x=t, t≠0
t²-5t+6=0
t₁=2, t₂=3
1. t₁=2, log₃x=2, <u>x₁=9</u>
2. t₂=3, log₃x=3. <u>x₂=27</u>
4 6/15+3 4/15=7 10/15=7 2/3
Ответ:
1 43/60.
Пошаговое объяснение:
Первый способ.
5 5/12 - 3 7/10 = (12*5 + 5)/12 - (10*3 + 7)/10 = 65/12 - 37/10 = 650/120 - 37*12/120 = 650/120 - 444/120 = (650 - 444)/120 = 206/120 = 103/60 = 1 43/60.
Второй способ.
5 5/12 - 3 7/10 = (5 - 3) + (5/12 - 7/10) = 2 + (50/120 - 84/120) = 2 - 34/120 = 1 + 1 - 34/120 = 1 + (1 - 17/60) = 1 43/60.