Answer:
[tex]ln(10)[/tex]
Step-by-step explanation:
Let's rewrite the expression as a single logarithm using the next propierties:
[tex]log(x*y)=log(x)+log(y)\\y*log(x)=log(x^{y} )\\log(\frac{x}{y} )=log(x)-log(y)[/tex]
So:
[tex]ln(5)+ln(32^{\frac{3}{5} } )-ln(4)[/tex]
Where:
[tex]32^{\frac{3}{5} }=\sqrt[5]{32^{3} } =\sqrt[5]{32768} =8[/tex]
Therefore:
[tex]ln(5)+ln(8)-ln(4)=ln(5*8)-ln(4)=ln(\frac{8*5}{4})=ln(\frac{40}{4})=ln(10)[/tex]
