Ecuații logaritmice Lesson Slides: 2 Slides (Grade 10)

2 Slides • 3 Questions

1

Ecuații logaritmice

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2

Exercițiul 1

\log_2x=\log_2\left(3x-1\right)

Urmăriți mai jos rezolvarea ecuației și descoperiți greșelile:
C.E.:

x\ge0,\ 3x-1\ge0

x\in\left(\frac{1}{3},+\infty\right)

x=3x-1

2x=-1

x=\frac{1}{2}\notin\left(\frac{1}{3},+\infty\right)

S=\left\{\frac{1}{2}\right\}

3

Multiple Select

Exercițiul 2

Care sunt condițiile de existență pentru logaritmul din ecuația: $\log_{x+2}\left(2x^3+5x+2\right)=1$

Selectați toate răspunsurile corecte de mai jos:

1

$x+2\ge0$

2

$x+2\ne1$

3

$2x^3+5x+2>0$

4

$2x^3+5x+2\ne1$

5

$x+2>0$

4

Multiple Choice

Exercițiul 3

Rezolvați ecuația $\log_5\left(2x-1\right)=2$ și alegeți varianta corespunzătoare soluției ecuației.

1

$S=\left\{\frac{33}{2}\right\}$

2

$S=\left\{13\right\}$

3

$S=\left\{\frac{3}{2}\right\}$

4

$S=\left\{\phi\right\}$

5

Multiple Choice

Exercițiul 4

Rezolvați ecuația $2\lg x=\lg\left(4x-3\right)\$ și alegeți varianta corectă din răspunsurile de mai jos:

1

$S=\left\{1\right\}$

2

$S=\left\{1,3\right\}$

Ecuații logaritmice

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