Question 132628
{{{log(10,(x+5))-log(10,(x+2))=log(10,(5))}}} Start with the given equation




{{{log(10,((x+5)/(x+2))=log(10,(5)))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}




*[Tex \LARGE 10^{\log _{10} \left( \frac{x+5}{x+2} \right)}=10^{\log _{10} \left(5 \right)}] Raise both sides as exponents with bases of 10. This will undo the logs



{{{(x+5)/(x+2)=5}}} Simplify



{{{x+5=5(x+2)}}} Multiply both sides by {{{x+2}}}



{{{x+5=5x+10}}} Distribute



{{{x=5x+10-5}}}Subtract 5 from both sides



{{{x-5x=10-5}}} Subtract 5x from both sides



{{{-4x=10-5}}} Combine like terms on the left side



{{{-4x=5}}} Combine like terms on the right side



{{{x=(5)/(-4)}}} Divide both sides by -4 to isolate x




{{{x=-5/4}}} Reduce


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Answer:

So our answer is {{{x=-5/4}}}  (which is approximately {{{x=-1.25}}} in decimal form)