Question 129924
{{{log(10,(x))+log(10,(x+3))=1}}} Start with the given equation


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



{{{10^(1)=x(x+3)}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{10=x(x+3)}}} Evaluate {{{10^(1)}}} to get {{{10}}}



{{{10=x^2+3x}}} Distribute



{{{0=x^2+3x-10}}} Subtract 10 from both sides



{{{0=(x+5)(x-2)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+5=0}}} or  {{{x-2=0}}} 


{{{x=-5}}} or  {{{x=2}}}    Now solve for x in each case



So our possible answers are

 {{{x=-5}}} or  {{{x=2}}} 




However, if you plug in {{{x=-5}}}, you'll have a negative number in the log.


So our only answer is {{{x=2}}}