Answer:
[tex]ln(\frac{8}{5x} )=ln(8)-ln(5)-ln(x)[/tex]
Step-by-step explanation:
Use the properties of logarithms on each step:
First use the property for the logarithm of a quotient:
[tex]ln(\frac{a}{b} )=ln(a)-ln(b)[/tex]
So we get: [tex]ln(\frac{8}{5x} )=ln(8)-ln(5x)[/tex]
Now, we can expand the last term using the property of logarithm of a product:
[tex]ln(a\,*\,b)=ln(a)+ln(b)[/tex]
Therefore we write [tex]ln(5x)=ln(5)+ln(x)[/tex]
No we insert this result in the subtraction we had before:
[tex]ln(\frac{8}{5x} )=ln(8)-ln(5x)=ln(8)-(ln(5)+ln(x))=ln(8)-ln(5)-ln(x)[/tex]
