Mi a megoldás? Matematika

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a) lg15

b) 3lg12

c) x=6

d) x=5

e) x=2

f) x=4

a)

2lg5 + 3lg2 - 20 = lg25 + lg8 - 20 = lg200 - 20 = lg200 - lg10^20 = lg(200/10^20) = lg(2*10^-18)

b)

2lg12 + lg625 - 2lg300 = lg144 + lg625 - lg90000 = lg144 + lg625 - lg90000 = lg90000 - lg90000 = lg1 = 0

c)

lg(2x+5) + lg(2-x) = 2lg(x+4)

lg((2x+5)*(2-x)) = lg((x+4)*(x+4))

lg(2*2x-2x*x+2*5-5x) = lg(x*x+4x+4x+4*4)

lg(-2x^2-x+10) = lg(x^2+8x+16)

-2x^2-x+10 = x^2+8x+16

-3x^2-9x-6 = 0

x = -2

x = -1

d)

2lg(×-2) = lg(4x+7) - lg3

lg((×-2)*(×-2)) = lg((4x+7)/3)

lg(×^2-4x+4) = lg((4/3)x+7/3)

×^2-4x+4 = (4/3)x+7/3

×^2-4x-(4/3)x+4-7/3 = 0

×^2-(16/3)x+5/3 = 0

x=5

x=1/3

e)

lg(48-3x) - lg(2-x) = 1

lg((48-3x)/(2-x)) = lg(10^1)

(48-3x)/(2-x) = 10^1

48-3x = 10*(2-x)

48-3x = 20-10x

48-20 = -10x+3x

28 = -7x

7x = -28

x = -28/7

x = -4

f)

lg(10+x) + lg(7-3x) = 2

lg((10+x)*(7-3x)) = 2

lg(70+7x-30x-3x^2) = 2

lg(-3x^2-23x+70) = 2

-3x^2-23x+70 = 10^2

-3x^2-23x+70-10^2 = 0

-3x^2-23x-30 = 0

x=-6

x=-5/3