285.
б) lnx < ln2
e>1
y=lnx - возрастает
{x>0
{x<2<br> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
------ 0 ------------- 2 ----------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 2)
д) ln3x≤ln6
e>1
y=lnx - возрастает
{3x>0
{3x≤6
{x>0
{x≤2
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---------0 ---------- 2 --------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 2]
286.
a) log₂ x>2
log₂ x>log₂ 2²
log₂ x>log₂ 4
2>1
y=log₂ x - возрастает
{x>0
{x>4
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-------- 0 ----------- 4 ------------
\\\\\\\\\\\\\\\\\\\
x∈(4; +∞)
б) log₂ x<3<br> log₂ x log₂ x2>1
y=log₂ x - возрастает
{x>0
{x<8<br> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---------0 ----------------8 ---------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 8)
в) lgx<0<br> lgx10>1
y=lgx - возрастает
{x>0
{x<1<br> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
----------0 -----------1 -----------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 1)
г) log₀.₂ x>1
log₀.₂ x> log₀.₂ 0.2
0.2<1<br>y=log₀.₂ x - убывает
{x>0
{x<0.2<br> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\
------ 0 ---------- 0.2 ----------
\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 0,2)
д) log₀.₂ x<0<br> log₀.₂ x0.2<1<br>у=log₀.₂ x - убывает
{x>0
{x>1
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-----0 ----------- 1 -----------
\\\\\\\\\\\\\\\\\\
x∈(1; +∞)
е) log₀.₅ x≥2
log₀.₅ x≥ log₀.₅ 0.5²
log₀.₅ x≥ log₀.₅ 0.25
0.5<1<br>у=log₀.₅ x - убывает
{x>0
{x≤0.25
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
------ 0 -----------0.25 -----------
\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(0; 0,25]