Question

log2= 0,3 e log3= 0,48. resolver equação: 10•(3)x = 6x. (3 e 6 tem X como expoente) ​

Answer 1

$10~.~3^x~=~6^x\\\\\\Aplicando~logaritmo~nos~dois~lados~da~equacao\\\\\\log\,\left(10~.~3^x\right)~=~log\,\left(6^x\right)\\\\\\Utilizando~a~propriedade~do~logaritmo~do~produto\\\\\\log\,10~+~log\,3^x~=~log\,6^x\\\\\\Utilizando~a~propriedade~do~logaritmo~do~expoente\\\\\\log\,10~+~x.log\,3~=~x.log6\\\\\\log\,10~+~x.log\,3~=~x.log\,(2~.~3)\\\\\\Utilizando~novamente~a~propriedade~do~logaritmo~do~produto\\\\\\log\,10~+~x.log\,3~=~x~.~(log\,2~+~log\,3)\\\\\\Substituindo~os~valores$

$1~+~x~.~0,48~=~x~.~(0,3~.~0,48)\\\\\\1~+~0,48x~=~0,78x\\\\\\0,30x~=~1\\\\\\x~=~\dfrac{1}{0,30}\\\\\\\boxed{x~=~\dfrac{10}{3}}$