Question

Imi poate explica si mie cineva cum se rezolva aceste exercitii? Multumesc frumos!

Answer 1

Răspuns:

1.2ˣ=64

2ˣ=2⁶

x=6

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3⁻ˣ=9

3⁻ˣ=3²

-x=2

x= -2

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3.)25ˣ=5ˣ⁺²

5²ˣ=5ˣ⁺²

2x=x+2

x=2

______________________

4)$\sqrt{5^x} =25^(x+4)$

5^(x/2)=5²⁽ˣ⁺⁴⁾

x/2=2(x+4)

x=4(x+4)

x=4x+4

x-4x=4

-3x=4

x= -4/3

________________________

5)log₂x=3

x=3²=9

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6.

log₂x+log₂10=log₂4

log₂10x=log₂2²

10x=2²

10x=4

x=4/10

______________________

7)log₃(x²-1)=2

Determini  mai  intai  DVA

x²-1>0

x²-1=0=>

x1= -1   x2=1

x∈(-∞,-1)U(1,∞)

Rezolvare

x²-1=3²

x²=1+9

x²=10

x=±√10∈DVA=>

x={-√10.+√10}

--------------------------------

8)√(x+1)=2

DVA

x+1≥0

x≥ -1

Ridici  ecuatia  la  patrat  si  obtii

√(x+1)²=2²

lx+1l=4

x+1=√4

x+1=±2

x1+1= -2

x1= -2-1= -3∉DVA

x2+1=2

x2=2-1

x2=1  solutie

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