Question

log10(x-9)+log10 100x=3

Answer 1

Log10(x-9)+log10 100x=3
log10[(x-9)(100x)]=3
(x-9)(100x)=10^3
100x^(2)-900x=1000
100x^(2)-900x-1000=0   aqui dividimos la expresion en 100
x^(2)-9x-10=0
(x-10)(x+1)=0
x=10
x=-1

las soluciones son esas
comprobamos
x=10
Log10(x-9)+log10 100x=3
Log10(10-9)+log10 (100*10)=3
0+3=3
3=3

con x=-1
Log10(-1-9)+log10 (100*(-1))=3
Log10(-10)+log10 (-100)=3

vemos que la -1 no es solucion al problema