Question

решите на множестве r уравнение
$\frac{1}{2} \times log_{ \frac{1}{25} }(5x + 2) ^{2} - log_{ \frac{1}{25} } \frac{1}{x - 1} = log_{ \frac{1}{25} }(6 - x) - log_{ \frac{1}{25} } \frac{1}{3}\ \textless \ br /\ \textgreater \ ​$

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Answer 1

Răspuns:

Explicație pas cu pas:

Nu mai scriem baza care este aceeasi peste tot.

log(5x+2)^2^(1/2) - log(1/(x-1) = log(6-x) -log(1/3)

Conditii:

5x +2 > 0,  x > -2/5

x-1 > 0 > x >1

6-x > 0 ,  x < 6

Deci x in (1, 6)

log((5x+2)/(1/(x-1)) = log((6-x)/(1/3))

((5x+2)*(x-1) = (6-x)*3

5x^2 -5x +2x -2 -18 +3x = 0

5x^2 = 2 +18 = 20

x^2 = 4

x = +- 2

x = 2 convine