Question

qual das opções abaixo apresenta o valor de x que é a solução da equação log2+log(x+1)-logx=1 :

a)0,15
b)0,25
c)0,35
d)0,45
e)0,55

Answer 1

log2 + log(x+1) - logx = 1

log2.(x+1)/x = 1

log2.(x+1)/x = log10

2.(x+1)/x = 10

x+1/x = 5

x+1 = 5x

4x = 1

x = 1/4 = 0,25 

Opção B.

Propriedades usadas :

*loga + logb = log(a.b)

*loga - logb = log(a/b)

Answer 2

$\mathsf{Ola\´~Caluiza,}$

$\mathsf{\log(2)+\log(x+1)-\log(x)=1 }\\\\\\\mathsf{Antes~precisamos~checar~a~condic\~ao~de~exist\^encia}\\\\\mathsf{C.E\begin{cases}x+1\ \textgreater \ 0~~|~~x\ \textgreater \ -1\\x\ \textgreater \ 0\end{cases}}\\\\\\\mathsf{x\ \textgreater \ -1~\bigcap~x\ \textgreater \ 0}\\\\\mathsf{C.E= \{x~\in~\mathbb{R}~|~x\ \textgreater \ 0\}}\\\\\\\mathsf{\log(\frac{2.(x+1)}{x})=1}\\\\\mathsf{\log(\frac{2x+2}{x})=log(10)}\\\\\mathsf{\frac{2x+2}{x}=10}\\\\\mathsf{2x+2=10x}\\\\\mathsf{8x=2}\\\\\mathsf{x=\frac{2}{8}}$


$\\\\\mathsf{\Large\boxed{x=0,25}}\\\\\\\mathsf{Resposta~alternativa~(b)}\\\\\mathsf{Du\´vidas?~comente}$