Question 143981
{{{log(10,(4x+1))-log(10,(2x-3))=2}}} Start with the given equation



{{{log(10,((4x+1)/(2x-3)))=2}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



{{{10^2=(4x+1)/(2x-3)}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{100=(4x+1)/(2x-3)}}} Square 10 to get 100



{{{100(2x-3)=4x+1}}} Multiply both sides by {{{2x-3}}}



{{{200x-300=4x+1}}} Distribute



{{{200x=4x+1+300}}}Add 300 to both sides



{{{200x-4x=1+300}}} Subtract 4x from both sides



{{{196x=1+300}}} Combine like terms on the left side



{{{196x=301}}} Combine like terms on the right side



{{{x=(301)/(196)}}} Divide both sides by 196 to isolate x




{{{x=43/28}}} Reduce


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Answer:

So our answer is {{{x=43/28}}}  (which is approximately {{{x=1.53571}}} in decimal form)