Question 152883
{{{log(10,(2x-1)) = log(10,(x+3)) + log(10,(3))}}} Start with the given equation.



{{{log(10,(2x-1)) = log(10,(3(x+3)))}}} Combine the logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{2x-1=3(x+3)}}} Set the inner arguments equal to one another.



{{{2x-1=3x+9}}} Distribute.



{{{2x=3x+9+1}}} Add {{{1}}} to both sides.



{{{2x-3x=9+1}}} Subtract {{{3x}}} from both sides.



{{{-x=9+1}}} Combine like terms on the left side.



{{{-x=10}}} Combine like terms on the right side.



{{{x=(10)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=-10}}} Reduce.



So the possible answer is {{{x=-10}}}; however, we must check it.


{{{log(10,(2x-1)) = log(10,(x+3)) + log(10,(3))}}} Start with the given equation.



{{{log(10,(2(-10)-1)) = log(10,(-10+3)) + log(10,(3))}}} Plug in {{{x=-10}}}



{{{log(10,(-13)) = log(10,(-7)) + log(10,(3))}}} Simplify. Since you <font size=4><b>cannot</b></font> take the log of negative number, this means that {{{x=-10}}} is <font size=4><b>not</b></font> a solution.


So there are no solutions.