Question

lnx-ln(x+4)=6

Answer 1

Hi,
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Answer 2

\[\Large\rm \ln x-\ln(x+4)=6\]The division rule for logs:\[\large\rm \color{orangered}{\ln a- \ln b=\ln\left(\frac{a}{b}\right)}\]Applying it to the left side of our equation gives us,\[\Large\rm \ln\left(\frac{x}{x+4}\right)=6\]

Answer 3

This is the log function of base e.
We'll convert it to exponential form.\[\Large\rm e^6=\frac{x}{x+4}\]Then you just have a few tricky algebra steps from there to solve for x.

Answer 4

Multiply both sides by x+4,\[\Large\rm (x+4)e^6=x\]Distribute the e^6 to each term in the brackets,\[\Large\rm x e^6+4e^6=x\]Subtract x e^6 from each side,\[\Large\rm 4e^6=x-x e^6\]Factor an x out of each term,\[\Large\rm 4e^6=x(1-e^6)\]Divide to finish solver for x.

Answer 5

Divide by 1-e^6 to finish solving for x*