Question

Resolva a equaçao logarítmica:

Answer 1

resolva: log2 (x+1) = log4 (x²+3)

log2 (x+1) = log4 (x²+3)

log2 (x+1) = log2 (x²+3)/log2 4

log2 (x+1) = log2 (x²+3)/2

(x²+3) = 2.(x+1)

x²+3 -2x -2 = 0

x² -2x +1 = 0

(x -1)² = 0

(x -1) = 0

x = 1 ✓

Answer 2

 Propriedade utilizada:

• $Log_{a^y}b^x$ <=> $\frac{x}{y}.Log_ab$

$Log_2(x+1)=Log_{2^2}(x^2+3)\\Log_2(x+1)=\frac{1}{2}.Log_2(x^2+3)\\2.Log_2(x+1)=Log_2(x^2+3)\\Log_2(x+1)^2=Log_2(x^2+3)\\\\(x+1)^2=x^2+3\\x^2+2.x+1=x^2+3\\2.x+1=3\\2.x=3-1\\2.x=2\\x=1$

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