Question 615686
solve log(x+20)-log(x+2)=logx


log (x + 20) - log (x + 2) = log x


log {{{((x + 20)/(x + 2))}}} = log {{{(x)}}}


{{{(x + 20)/(x + 2) = x}}}


x(x + 2) = x + 20 ----- Cross-multiplying


{{{x^2 + 2x = x + 20}}}


{{{x^2 + 2x - x - 20 = 0}}}


{{{x^2 + x - 20 = 0}}}


(x + 5)(x - 4) = 0


x + 5 = 0  or x - 4 = 0


x = - 5 (EXTRANEOUS) or x = {{{highlight_green(4)}}}


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Check
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log (x + 20) - log (x + 2) = log x


log (4 + 20) - log (4 + 2) = log 4 ------ Substituting 4 for x in original equation


log (24) - log (6) = log 4


log {{{(24)/6}}} = log {{{4}}}


log (4) = log 4 (TRUE)

 
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