Question 142208


{{{ln(x)-ln(x+7)=-1}}} Start with the given equation




{{{ln((x)/(x+7))=-1}}} Combine the logs using the identity {{{ln(A)-ln(B)=ln(A/B)}}}




{{{e^(-1)=(x)/(x+7)}}} Use the property {{{ln(x)=y}}} ==> {{{e^y=x}}} to rewrite the equation




{{{1/e=(x)/(x+7)}}} Rewrite {{{e^(-1)}}} as {{{1/e}}}




{{{x+7=ex}}} Cross Multiply



{{{7=ex-x}}} Subtract x from both sides



{{{7=x(e-1)}}} Factor out the GCF x



{{{7/(e-1)=x}}} Divide both sides by {{{e-1}}}




So our answer is {{{x=7/(e-1)}}} which is approximately {{{x=4.07384}}}