Answer:
[tex]x=\frac{6e^3}{e^3-1}[/tex]
Step-by-step explanation:
[tex]ln x - ln(x - 6) = 3[/tex]
Apply natural log property
ln mn=ln m + ln(n), ln(m/n)=ln(m)-ln(n)
[tex]ln x - ln(x - 6) = 3[/tex]
[tex]ln(\frac{x}{x-6} )=3[/tex]
All natural log has base 'e'
[tex]\frac{x}{x-6} =e^3[/tex]
cross multiply
[tex]x=e^3(x-6)[/tex]
[tex]x=e^3x-6e^3[/tex]
add 6e^3 on both sides and -x on both sides
[tex]6e^3=e^3x-x[/tex]
[tex]6e^3=x(e^3-1)[/tex]
Divide e^3-1 on both sides
[tex]x=\frac{6e^3}{e^3-1}[/tex]
