Question

Write as a single logarithm. ln(5) + 3/5 ln(32) − ln(4)

Answer 1

Answer:

$ln(10)$

Step-by-step explanation:

Let's rewrite the expression as a single logarithm using the next propierties:

$log(x*y)=log(x)+log(y)\\y*log(x)=log(x^{y} )\\log(\frac{x}{y} )=log(x)-log(y)$

So:

$ln(5)+ln(32^{\frac{3}{5} } )-ln(4)$

Where:

$32^{\frac{3}{5} }=\sqrt[5]{32^{3} } =\sqrt[5]{32768} =8$

Therefore:

$ln(5)+ln(8)-ln(4)=ln(5*8)-ln(4)=ln(\frac{8*5}{4})=ln(\frac{40}{4})=ln(10)$