Question 750046
{{{0.2^(x+1)=3^(x)}}}


{{{log(0.2^(x+1))=log(3^(x))}}}

{{{(x+1)*log(0.2)=x*log(3)}}}

{{{x*log(0.2)+log(0.2)=x*log(3)}}}

Combining steps next
{{{x*log(0.2)-x*log(3)=-log(0.2)}}}

Multiplying both sides by negative 1
and reverse-distribute the x,
{{{x(log(3)-log(0.2))=log(0.2)}}}


{{{highlight(x=(log(0.2))/((log(3)-log(0.2))))}}}