a)log2(2x-1) = 2
2x-1 = 2²
2x-1 = 4
2x = 5
x = 2.5
Ответ: {2.5}
б)log3(x+2)+log3(x) = 1
ОДЗ:
{x > -2
{x > 0
x > 0
log3(x(x+2)) = log3(3)
x²+2x = 3
x²+2x-3 = 0
По теореме Виета:
x1 = 1
x2 = -3
Ответ: {1}
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Answers & Comments
a)log2(2x-1) = 2
2x-1 = 2²
2x-1 = 4
2x = 5
x = 2.5
Ответ: {2.5}
б)log3(x+2)+log3(x) = 1
ОДЗ:
{x > -2
{x > 0
x > 0
log3(x(x+2)) = log3(3)
x²+2x = 3
x²+2x-3 = 0
По теореме Виета:
x1 = 1
x2 = -3
Ответ: {1}