Question

Urgente,2log(x-1)=log(x-1)+log2, log2(x+4)-log2(x-4)=1 , log2(x+3)-2log2 2=2 , log x²-log x=1 , log3(x-2)+log3 3=1

Answer 1

Ola Marta

2log(x - 1) = log(x - 1) + log(2) 

log((x - 1)²) = log(2x - 2)

x² - 2x + 1 = 2x - 2

x² - 4x + 3 = 0

delta
d² = 16 - 12 = 4
d = 2

x1 = (4 + 2)/2 = 3
x2 = (4 - 2)/2 = 1 não serve

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log2(x + 4) - log2(x - 4) = 1

log2( /x + 4)/(x - 4)) = log2(2)

x + 4 = 2x - 8

x = 12

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log2(x + 3) - 2log2(2) = 2

log2( (x + 3)/4 ) = log2(4)

(x + 3)/4 = 4
x + 3 = 16
x = 13

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log(x²) - log(x)  1

2log(x) - log(x) = 1

log(x) = 1 = log(10)

x = 10 

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log3(x - 2) + log3(3) = 1 

log3(x - 2) + 1 = 1

log3( x - 2)= 0

log3(x - 2) = log3(1)

x - 2 = 1
x = 3

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