Question 119567
{{{log(10,(3-2x))-log(10,(x+9))=0}}} Start with the given equation.  Note: Since you did not specify a base, this means that we're going to use the default base 10.


{{{log(10,((3-2x)/(x+9)))=0}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}





{{{10^(0)=(3-2x)/(x+9)}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{1=(3-2x)/(x+9)}}} Evaluate {{{10^(0)}}} to get {{{1}}}



{{{x+9=3-2x}}} Multiply both sides by {{{x+9}}}




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



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



{{{3x=3-9}}} Combine like terms on the left side



{{{3x=-6}}} Combine like terms on the right side



{{{x=(-6)/(3)}}} Divide both sides by 3 to isolate x




{{{x=-2}}} Divide


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Answer:

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