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Tatiana Subbotina
Помогите пожалуйста!!!! Сколько целых решений имеет неравенство?
Эдвард Гладкий
Ответ
log(8) {x+1} + log(1/2) {x+1} >= -2/3
ОДЗ: x+1>0 => x > -1
log(2^3) {x+1} + log(2^(-1)) {x+1} >= -2/3
log(2^3) {x+1} + log(2^(-1)) {x+1} >= -2/3
(1/3)*log(2) {x+1} + (1/(-1))log(2) {x+1} >= -2/3
log(2) {x+1}^(1/3) - log(2) {x+1} >= -2/3
log(2) {(x+1)^(1/3) / (x+1)} >= -2/3
log(2) {(x+1)^(1/3) / (x+1)} >= log(2) {2^(-2/3)}
(x+1)^(1/3) / (x+1) >= 2^(-2/3)
(x+1)^(1/3-1) >= 2^(-2/3)
(x+1)^(-2/3) >= 2^(-2/3)
x+1 >= 2
x >= 2-1
x >= 1
ОЛ
Оксана Лебедева
Ответ
log(8) {x+1} + log(1/2) {x+1} >= -2/3
ОДЗ: x+1>0 => x > -1
log(2^3) {x+1} + log(2^(-1)) {x+1} >= -2/3
log(2^3) {x+1} + log(2^(-1)) {x+1} >= -2/3
(1/3)*log(2) {x+1} + (1/(-1))log(2) {x+1} >= -2/3
log(2) {x+1}^(1/3) - log(2) {x+1} >= -2/3
log(2) {(x+1)^(1/3) / (x+1)} >= -2/3
log(2) {(x+1)^(1/3) / (x+1)} >= log(2) {2^(-2/3)}
(x+1)^(1/3) / (x+1) >= 2^(-2/3)
(x+1)^(1/3-1) >= 2^(-2/3)
(x+1)^(-2/3) >= 2^(-2/3)
x+1 >= 2
x >= 2-1
x >= 1
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