U kom intervalu se nalazi najmanje rešenje jednačine: 1 6 1 x = 4 x 2 ? 16^{\frac{1}{x}}=4^{\frac{x}{2}}\ \ ? 1 6 x 1 = 4 2 x ?

( − 3 , 0 ) \left(-3,0\right) ( − 3 , 0 )

( − ∞ , − 3 ) \left(-\infty,-3\right) ( − ∞ , − 3 )

( 0 , 3 ) \left(0,3\right) ( 0 , 3 )

( 3 , 5 ) \left(3,5\right) ( 3 , 5 )

( 5 , + ∞ ) \left(5,+\infty\right) ( 5 , + ∞ )

Kom intervalu pripada rešenje jednačine: 2 5 x + 1 5 − 4 2 x − 5 3 = 5 2 x − 3 5 + 4 2 x − 2 3 ? 25^{\frac{x+1}{5}}-4^{\frac{2x-5}{3}}=5^{\frac{2x-3}{5}}+4^{\frac{2x-2}{3}}\ \ ? 2 5 5 x + 1 − 4 3 2 x − 5 = 5 5 2 x − 3 + 4 3 2 x − 2 ?

( 3 , + ∞ ) \left(3,+\infty\right) ( 3 , + ∞ )

( − ∞ , − 3 ) \left(-\infty,-3\right) ( − ∞ , − 3 )

( − 3 , 0 ) \left(-3,0\right) ( − 3 , 0 )

( 0 , 3 ) \left(0,3\right) ( 0 , 3 )

Proizvod rešenja jednačine ( 3 + 2 2 ) x + ( 3 − 2 2 ) x = 34 j e : \left(\sqrt{3+2\sqrt{2}}\right)^x+\left(\sqrt{3-2\sqrt{2}}\right)^x=34\ \ \ je: ( 3 + 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> <path d="M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7, 572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7, -7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39 c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60 s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5, -658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z M1001 80H400000v40H1013z"> ) x + ( 3 − 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> <path d="M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7, 572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7, -7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39 c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60 s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5, -658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z M1001 80H400000v40H1013z"> ) x = 3 4 j e :

12 2 − 34 12\sqrt{2}-34 1 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 3 4

Skup rešenja nejednačine ( 1 5 ) ∣ 2 x − 6 ∣ ≥ 5 x − 7 25 j e : \left(\frac{1}{5}\right)^{\left|2x-6\right|}\ge\frac{5^{x-7}}{25}\ \ \ je: ( 5 1 ) ∣ 2 x − 6 ∣ ≥ 2 5 5 x − 7 j e :

[ − 3 , 5 ] \ \left[-3,5\right] [ − 3 , 5 ]

( − ∞ , 5 ] \left(-\infty,5\right] ( − ∞ , 5 ]

[ 5 , + ∞ ) \left[5,+\infty\right) [ 5 , + ∞ )

Skup rešenja nejednačine 2 x + 2 − x + 1 − 3 < 0 j e : 2^x+2^{-x+1}-3<0\ \ \ je: 2 x + 2 − x + 1 − 3 < 0 j e :

( 0 , 1 ) \left(0,1\right) ( 0 , 1 )

( − ∞ , 0 ) ∪ ( 1 , + ∞ ) \left(-\infty,0\right)\cup\left(1,+\infty\right) ( − ∞ , 0 ) ∪ ( 1 , + ∞ )

( 1 , + ∞ ) \left(1,+\infty\right) ( 1 , + ∞ )

( − ∞ , 0 ) \left(-\infty,0\right) ( − ∞ , 0 )

( 2 , + ∞ ) \left(2,+\infty\right) ( 2 , + ∞ )

Eksponencijalne jednačine i nejednačine

Authored by Јованка Стојковић

Mathematics

2nd Grade

Used 36+ times

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Rešenje jednačine
$12^{3x-18}=144^x$

-2

-18

FILL IN THE BLANKS QUESTION

5 mins • 1 pt

Rešenje jednačine
$3^{2x}+9=6\cdot3^x$ je (upiši samo broj):

(a)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Rešenje jednačine
$9^x+6^x=2\cdot4^{x\ \ }\ \ je:$

1,5

$\frac{2}{3}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Skup rešenja jednačine
$4^{x^2}-0,25=0\ \ je:$

prazan

jednočlan

dvočlan

tročlan

beskonačan

MULTIPLE SELECT QUESTION

5 mins • 1 pt

U kom intervalu se nalazi najmanje rešenje jednačine:
$16^{\frac{1}{x}}=4^{\frac{x}{2}}\ \ ?$

$\left(-\infty,-3\right)$

$\left(-3,0\right)$

$\left(0,3\right)$

$\left(3,5\right)$

$\left(5,+\infty\right)$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Koliko rešenja ima jednačina
$\sqrt{2}\cdot0,5^{\frac{5}{4\sqrt{x}+10}}=4^{\frac{1}{\sqrt{x}+1}}\ \ ?$

više od 3

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Kom intervalu pripada rešenje jednačine:
$25^{\frac{x+1}{5}}-4^{\frac{2x-5}{3}}=5^{\frac{2x-3}{5}}+4^{\frac{2x-2}{3}}\ \ ?$

$\left(-\infty,-3\right)$

$\left(-3,0\right)$

$\left(0,3\right)$

$\left(3,+\infty\right)$

jednačina nema rešenja

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Proizvod rešenja jednačine
$\left(\sqrt{3+2\sqrt{2}}\right)^x+\left(\sqrt{3-2\sqrt{2}}\right)^x=34\ \ \ je:$

$12\sqrt{2}-34$

-12

-16

-4

-8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Skup rešenja nejednačine
$\left(\frac{1}{5}\right)^{\left|2x-6\right|}\ge\frac{5^{x-7}}{25}\ \ \ je:$

prazan

$\ \left[-3,5\right]$

$\left(-\infty,5\right]$

$\left[5,+\infty\right)$

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Skup rešenja nejednačine
$2^x+2^{-x+1}-3<0\ \ \ je:$

$\left(0,1\right)$

$\left(-\infty,0\right)\cup\left(1,+\infty\right)$

$\left(1,+\infty\right)$

$\left(-\infty,0\right)$

$\left(2,+\infty\right)$

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Eksponencijalne jednačine i nejednačine

Rešenje jednačine 123x−18=144x12^{3x-18}=144^x123x−18=144x

Rešenje jednačine 32x+9=6⋅3x3^{2x}+9=6\cdot3^x32x+9=6⋅3x je (upiši samo broj): (a)

Rešenje jednačine 9x+6x=2⋅4x je:9^x+6^x=2\cdot4^{x\ \ }\ \ je:9x+6x=2⋅4x je:

Skup rešenja jednačine 4x2−0,25=0 je:4^{x^2}-0,25=0\ \ je:4x2−0,25=0 je:

U kom intervalu se nalazi najmanje rešenje jednačine: 161x=4x2 ?16^{\frac{1}{x}}=4^{\frac{x}{2}}\ \ ?16x1​=42x​ ?

Koliko rešenja ima jednačina 2⋅0,554x+10=41x+1 ?\sqrt{2}\cdot0,5^{\frac{5}{4\sqrt{x}+10}}=4^{\frac{1}{\sqrt{x}+1}}\ \ ?2​⋅0,54x​+105​=4x​+11​ ?

Kom intervalu pripada rešenje jednačine: 25x+15−42x−53=52x−35+42x−23 ?25^{\frac{x+1}{5}}-4^{\frac{2x-5}{3}}=5^{\frac{2x-3}{5}}+4^{\frac{2x-2}{3}}\ \ ?255x+1​−432x−5​=552x−3​+432x−2​ ?

Proizvod rešenja jednačine (3+22)x+(3−22)x=34 je:\left(\sqrt{3+2\sqrt{2}}\right)^x+\left(\sqrt{3-2\sqrt{2}}\right)^x=34\ \ \ je:(3+22​​)x+(3−22​​)x=34 je:

Skup rešenja nejednačine (15)∣2x−6∣≥5x−725 je:\left(\frac{1}{5}\right)^{\left|2x-6\right|}\ge\frac{5^{x-7}}{25}\ \ \ je:(51​)∣2x−6∣≥255x−7​ je:

Skup rešenja nejednačine 2x+2−x+1−3<0 je:2^x+2^{-x+1}-3<0\ \ \ je:2x+2−x+1−3<0 je:

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Rešenje jednačine
$12^{3x-18}=144^x$

Rešenje jednačine
$3^{2x}+9=6\cdot3^x$ je (upiši samo broj):

(a)

Rešenje jednačine
$9^x+6^x=2\cdot4^{x\ \ }\ \ je:$

Skup rešenja jednačine
$4^{x^2}-0,25=0\ \ je:$

U kom intervalu se nalazi najmanje rešenje jednačine:
$16^{\frac{1}{x}}=4^{\frac{x}{2}}\ \ ?$

Koliko rešenja ima jednačina
$\sqrt{2}\cdot0,5^{\frac{5}{4\sqrt{x}+10}}=4^{\frac{1}{\sqrt{x}+1}}\ \ ?$

Kom intervalu pripada rešenje jednačine:
$25^{\frac{x+1}{5}}-4^{\frac{2x-5}{3}}=5^{\frac{2x-3}{5}}+4^{\frac{2x-2}{3}}\ \ ?$

Proizvod rešenja jednačine
$\left(\sqrt{3+2\sqrt{2}}\right)^x+\left(\sqrt{3-2\sqrt{2}}\right)^x=34\ \ \ je:$

Skup rešenja nejednačine
$\left(\frac{1}{5}\right)^{\left|2x-6\right|}\ge\frac{5^{x-7}}{25}\ \ \ je:$

Skup rešenja nejednačine
$2^x+2^{-x+1}-3<0\ \ \ je:$