Answer:
7v - 5u
Step-by-step explanation:
Our expression is: [tex]ln(\frac{y^7}{x^5} )[/tex]. Remember the property of ln, where ln(a / b) = ln(a) - ln(b). We can apply that here:
[tex]ln(\frac{y^7}{x^5} )[/tex] = ln([tex]y^7[/tex]) - ln([tex]x^5[/tex])
Now, also remember that when we have ln([tex]a^b[/tex]), we can write it as b * ln(a). Apply this here:
ln([tex]y^7[/tex]) = 7ln(y)
ln([tex]x^5[/tex]) = 5ln(x)
Notice that since u = ln(x) and v = ln(y), we can replace those respectively:
7ln(y) = 7v
5ln(x) = 5u
Put it together:
[tex]ln(\frac{y^7}{x^5} )[/tex] = 7v - 5u
