Αν Α,Β>0 και α,b>0 , a , b ≠ 1 a,b\ne1 a , b  = 1 ισχύει

log ⁡ a A = log ⁡ b A log ⁡ b a \log_aA=\frac{\log_bA}{\log_ba} lo g a A = lo g b a lo g b A

log ⁡ a A = log ⁡ b a log ⁡ b A \log_aA=\frac{\log_ba}{\log_bA} lo g a A = lo g b A lo g b a

Ιδιότητες Λογαρίθμων Quiz: 7 Practice Questions (Grade 11)

7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Αν Α ,Β>0 και $α>0,\ α\ne1$ ισχύει $\log_aA-\log_aB=\log_a\ \left(\frac{A}{B}\right)$

ΣΩΣΤΌ

ΛAΘΟΣ

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Αν A, B> 0 και $α,b>0,\ α,b\ne1$ ισχύει $\log_aΑ+\log_bB=\log_{ab}\ \left(A\cdotΒ\right)$

ΣΩΣΤΌ

ΛΆΘΟΣ

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ποιό απο τα πιο κάτω αληθεύει;

log100= -2

log100= 2

$\log100=\frac{1}{2}$

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Αν x>0 ισχύει $\frac{1}{2}\log x=\log\sqrt{x}$

ΣΩΣΤΟ

ΛΑΘΟΣ

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η συνάρτηση με τύπο $f\left(x\right)=\log\left(x+5\right)$ ορίζεται αν

x ανήκει στους πραγματικούς αριθμούς

x > -5

x < -5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Αν Α,Β>0 και α,b>0 , $a,b\ne1$ ισχύει

$\log_aA=\frac{\log_ba}{\log_bA}$

$\log_aA=\frac{\log_bA}{\log_ba}$

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η λογαριθμική συνάρτηση είναι ένα προς ένα.

Σωστό

Λάθος

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Ιδιότητες Λογαρίθμων

Αν Α ,Β>0 και α>0, α≠1α>0,\ α\ne1α>0, α​=1 ισχύει log⁡aA−log⁡aB=log⁡a (AB)\log_aA-\log_aB=\log_a\ \left(\frac{A}{B}\right)loga​A−loga​B=loga​ (BA​)

Αν A, B> 0 και α,b>0, α,b≠1α,b>0,\ α,b\ne1α,b>0, α,b​=1 ισχύει log⁡aA+log⁡bB=log⁡ab (A⋅B)\log_aΑ+\log_bB=\log_{ab}\ \left(A\cdotΒ\right)loga​A+logb​B=logab​ (A⋅B)

Ποιό απο τα πιο κάτω αληθεύει;

Αν x>0 ισχύει 12log⁡x=log⁡x\frac{1}{2}\log x=\log\sqrt{x}21​logx=logx​

Η συνάρτηση με τύπο f(x)=log⁡(x+5)f\left(x\right)=\log\left(x+5\right)f(x)=log(x+5) ορίζεται αν

Αν Α,Β>0 και α,b>0 , a,b≠1a,b\ne1a,b​=1 ισχύει

Η λογαριθμική συνάρτηση είναι ένα προς ένα.

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Discover more resources for Mathematics

Αν Α ,Β>0 και $α>0,\ α\ne1$ ισχύει $\log_aA-\log_aB=\log_a\ \left(\frac{A}{B}\right)$

Αν A, B> 0 και $α,b>0,\ α,b\ne1$ ισχύει $\log_aΑ+\log_bB=\log_{ab}\ \left(A\cdotΒ\right)$

Αν x>0 ισχύει $\frac{1}{2}\log x=\log\sqrt{x}$

Η συνάρτηση με τύπο $f\left(x\right)=\log\left(x+5\right)$ ορίζεται αν

Αν Α,Β>0 και α,b>0 , $a,b\ne1$ ισχύει