1. (27^(2/5) * 2^(1/5)*2)^(5/6) = (27^(2/5) * 2^(6/5))^(5/6) = ((3^6)^(2/5)* 2^(6/5))^(5/6) = 3^(12/5 * 5/6) * 2^(6/5 * 5/6) = 3^2 * 2 = 9 * 2 = 18
2.
2^(2x) - 3 * 2^(x+1) + 8 = 0
2^(2x) - 6 * 2^(x) + 8 = 0
пусть 2^x = t, t > 0
t^2 - 6t + 8 = 0
D = 36-4*1*8 = 4
t1 = (6+2)/2 = 4
t2 = 4/2 = 2
2^x = 4
x1 = 2
2^x = 2
x2 = 1
3. sqrt4 (625 * 0.0016) = sqrt4 (5^4 * 0.2^4) = 5 * 0.2 = 1
5. sqrt (5-2x) - 1 = -x
ОДЗ:
{5-2x >=0
{1-x >=0
{-2x >= -5
{-x >= -1
{x <= 2.5<br>{x<= 1<br>
x<=1<br>
sqrt (5-2x) = 1-x
5 - 2x = 1 -2x + x^2
x^2 = 4
x1 = 2 - не удовл. ОДЗ
x2 = -2
6. log 0.1 (x-3) <= 2<br>ОДЗ: x-3 >0
x > 3
log 0.1 (x-3) <= log 0.1 0.1^3<br>x - 3 > = 0.001
x >= 3.001
{x > 3
{x >= 3.001
x >= 3.001