Question

Encontrar el valor de x? log(x-9)+log100x=3

Answer 1

$\log(x-9)+\log100x=3\\ D:x-9>0 \wedge 100x>0\\ D:x>9 \wedge x>0\\ D:x>9\\ \log100x(x-9)=3\\ 10^3=100x(x-9)\\ 10=x(x-9)\\ x^2-9x-10=0\\ x^2+x-10x-10=0\\ x(x+1)-10(x+1)=0\\ (x-10)(x+1)=0\\ x=10 \vee x=-1\\ -1\not \in D \Rightarrow x=10$