13.
lg (x² -2x) > lg 3
{x²-2x>0
{x²-2x>3
x²-2x>0
x(x-2)>0
x=0 x=2
+ - +
---------- 0 ---------- 2 --------------
\\\\\\\\\\ \\\\\\\\\\\\\\\\
x<0 и x>2
x²-2x>3
x²-2x-3>0
x²-2x-3=0
D=4+12=16
x₁=2-4=-1
2
x₂=2+4=3
2
+ - +
------------- -1 -------------- 3 --------------
\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\
x<-1 и x>3
\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
----------- -1 ------- 0 ------------------- 2 --------- 3 -----------------
\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\
x<-1 и x>3
Ответ: x<-1<br> x>3
14.
0.2^(x²-6x-7)≥1
0.2^(x²-6x-7)≥0.2⁰
так как 0,2<1, то<br>x²-6x-7≤0
x²-6x-7=0
D=36+28=64
x₁=6-8= -1
2
x₂=6+8=7
2
+ - +
------------- -1 -------------- 7 ---------------
\\\\\\\\\\\\\\\
x∈[-1; 7]
Ответ: -1≤х≤7
7. log₄ X = log₄ 32 - log₄ 2
log₄ X= log₄ (32/2)
log₄ X= log₄ 16
x=16
Ответ: 16
8. log₇ x=4 log₇ 2 - 2 log₇ 1
log₇ x= log₇ 2⁴ - log₇ 1²
log₇ x= log₇ (16/1)
x=16
Ответ: 16
9. log₄ x=log₄ 13 + log₄ (7/13)
log₄ x=log₄ (13 * (7/13))
log₄ x=log₄ 7
x=7
Ответ: 7
10.
log₂ x=log₂ 4 + log₂ 7 - log₂ 2 - log₂ 7
log₂ x=(log₂ 4 + log₂ 7) - (log₂ 2 + log₂ 7)
log₂ x= log₂ (4*7) - log₂ (2*7)
log₂ x=log₂ (28/14)
log₂ x=log₂ 2
x=2
Ответ: 2.