Answer:
[tex]x=\frac{-5*(1+e^{3}) }{10-e^{3} }[/tex]
Step-by-step explanation:
Rewrite the equation, adding 3 to both sides and subtracting log(x-5) from both sides:
[tex]log(10x+5)-log(x-5)=3[/tex]
Using the next propierty:
[tex]log(\frac{1}{x} )=-log(x)[/tex]
[tex]log(10x+5)+log(\frac{1}{x-5})=3[/tex]
Using this propierty:
[tex]log(x*y)=log(x)+log(y)[/tex]
[tex]log(\frac{10x+5}{x-5})=3[/tex]
Cancel logarithms by taking exp of both sides:
[tex]e^{log(\frac{10x+5}{x-5})} =e^{3} \\\frac{10x+5}{x-5}=e^{3}[/tex]
Multiplying both sides by x-5 and factoring:
[tex]x(10-e^{3} )=-5-5e^{3}[/tex]
Solving for x multiplying both sides by [tex]10-e^{3}[/tex]
[tex]x=\frac{-5-5e^{3} }{10-e^{3} } =\frac{-5*(1+e^{3}) }{10-e^{3} }[/tex]
