Question 110929
{{{log(10,(x+4))-log(10,(x-3))=log(10,(8))}}} Start with the given equation



{{{log(10,((x+4)/(x-3)))=log(10,(8))}}} Combine the logs using the identity {{{log(a)-log(b)=log(a/b)}}}



{{{(x+4)/(x-3)=8}}} Since the bases are equal, the arguments are equal



{{{x+4=8(x-3)}}} Multiply both sides by x-3 



{{{x+4=8x-24}}} Distribute




{{{x=8x-24-4}}}Subtract 4 from both sides



{{{x-8x=-24-4}}} Subtract 8x from both sides



{{{-7x=-24-4}}} Combine like terms on the left side



{{{-7x=-28}}} Combine like terms on the right side



{{{x=(-28)/(-7)}}} Divide both sides by -7 to isolate x




{{{x=4}}} Divide


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Answer:

So our answer is {{{x=4}}}