Question

Calcule 20^x+3(10)^x=4 demonstrando os passos.

Answer 1

$20^x+3.10^x=4\\\\ 2^x.10^x+3.10^x=4\\\\ 10^x(2^x+3)=4\\\\ Como \ 4=1.4 \ ou \ 4=2.2, \ temos:\\\\ 1\ª \ possibilidade:\\\\ 10^x(2^x+3)=1.4\\\\ 10^x=1 \ \implies \ x=0\\\\ e\\\\ 2^x+3=4\\\\ 2^x=4-3\\\\ 2^x=1 \ \implies x=0 \ (este \ valor \ solucioana)$


$2\ª \ possibilidade:\\\\ 10^x(2^x+3)=2.2\\\\ 10^x=2 \ \implies \ x=log2 \ (este \ valor \ n\~ao \ solucioana)\\\\ e\\\\ 2^x+3=2\\\\ 2^x=2-3\\\\ 2^x=-1 \ \implies \ n\~ao \ existe \ x$


$Para \ a \ possibilidade \ 4=4.1 \temos:\\\\ 10^x(2^x+3)=4.1\\\\ 10^x=4 \ \implies \ x=log4 \ (este \ valor \ n\~ao \ soluciona) \\\\ e\\\\ 2^x+3=1\\\\ 2^x=1-3\\\\ 2^x=-2 \ \implies \ x \ n\~ao \ existe$