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axen
user (0)
Pe: 2012-11-04T09:29:33+02:00 In: In:

Problema Algebra

Aflati x din egalitatile
a) 3 la.puterea x-2=81
B)5 la.puterea 2x-1=125
c) 4 la.puterea 2x+2=16la.puterea2
d) (2supra3) la.puterea 2x+3 : (2supra3) la.puterea x+1 = (6supra9) la.puterea 2
e) 8 la.puterea 2x+1 + 8 la.puterea 2x = 9x2la.puterea 2010
f)5la.puterea x + 5 la puterea x+1 + 5la.puterea x+2= 775
.

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5 raspunsuri

  1. gixgex
    user (0)

    substitui exponentul cu y
    aflii y
    apoi scrii y(valoarea aflata)=exponentul cerut
    aflii x

    ex:
    a.
    x-2=y
    3^y=81
    y=4
    4=x-2
    x=6

    • 0
  2. axen
    user (0)

    GREU FOARTE GREU , IMI FACI REZOLVAREA :s ?

    • 0
  4. dan
    expert (VI)

    axen wrote: Aflati x din egalitatile
    a) 3 la.puterea x-2=81
    B)5 la.puterea 2x-1=125
    c) 4 la.puterea 2x+2=16la.puterea2
    d) (2supra3) la.puterea 2x+3 : (2supra3) la.puterea x+1 = (6supra9) la.puterea 2
    e) 8 la.puterea 2x+1 + 8 la.puterea 2x = 9x2la.puterea 2010
    f)5la.puterea x + 5 la puterea x+1 + 5la.puterea x+2= 775
    .


    \rm{ Se aplica formula: \fbox{ a^m : a^n = a^{m-n} }\re
    \rm{ adica: \\ a). 3^{x-2}=81 \leftrightarrow 3^x : 3^2=81 \\ \rightarrow 3^x=81 \cdot 3^2 = 9^2\cdot 9 = (3^2)^2 \cdot 3^2 = 3^6 \rightarrow \fbox{ x=6 };\\ ..................................................................................................................\\ f). 5^x + 5^{x+1} + 5^{x+2} = 775 dam factor comun pe " 5^x" ... \\ obtinem: ... 5^x\cdot (1+5^1+5^2) = 5^x \cdot 31 = 775 \\ \rightarrow 5^x = 775:31 \Rightarrow 5^x = 25 etc.

    • 0
  5. doctal
    user (0)

    axen wrote: Aflati x din egalitatile
    a) 3 la.puterea x-2=81
    B)5 la.puterea 2x-1=125

    .

    \rm{{\Large\bl 3^{x-2} = 81 \Rightarrow 3^{x-2} = 3^4 \Rightarrow x-2 = 4 \Rightarrow x = 6.\\ 5^{2x-1} = 125 \Rightarrow 5^{2x-1} = 5^3 \\ \Rightarrow 2x-1 = 3 \Rightarrow 2x = 4 \Rightarrow x = 2.

    • 0
  6. doctal
    user (0)

    axen wrote: Aflati x din egalitatile

    c) 4 la.puterea 2x+2=16la.puterea2
    .

    \rm{ 4^{2x+2} = 16^2} \Rightarrow 4^{2x+2} = (4^2)^2 \\ \Rightarrow 4^{2x+2 = 4^4 \Rightarrow 2x+2 = 4

    • 0
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