Question

resolva as equações logarítmicas

Answer 1

A)

$Log_{3}(3x+12)=4$

$(3x+12)=3^4$

$(3x+12)=81$

$3x+12=81$

$3=0\:Ou\:x-23=0$

Nenhuma solução ou x=23.

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B)

$Log_{3}(x+1)+Log_{3}(x-7)=2$

$Log_{3}(x+1)(x-7)=2$

$(x+1)(x-7)=3^2$

$x^2-6x-16=0$

$x+2=0\:\:V\:\:x-8=0$

$x=-2\:\:V\:\:x=8$

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C)

$1-log_{2}x=Log_{2}(x+1)$

$-log_{2}x+1=log_{2}(x+1)$

$-log_{2}x=log_{2}(x+1)$

$log_{2}x=log_{2}(x+1)-1$

$log_{2}x=-log_{2}(x+1)+1$

$x=2^{-log_{2}(x+1)+1}$

$x=2^{-log_{2}(x+1)}.2^1$

$(x+1)^{-1}.2$

$x=\frac{1}{(x+1)^1}.2$

$x=\frac{1.2}{(x+1)^1}$

$(x+1)x=1.2$

$x^2+x.1=2$

$x^2+x-2=0$

$x-1=0\:Ou\:x+2=0$

$x=1\:Ou\:x=-2$

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