Question

Expand the logarithm. ln((-3e^5)/(x^3))

Answer 1

Answer:

ln(3) + 5 - 3ln(x) or 6.0986 - 3ln(x)

Step-by-step explanation:

$ln(\frac{3e^{5} }{x^3} )$

$ln(\frac{3e^{5} }{x^3} )$ = $ln(3e^5)-ln(x^3)$, since ln(x/y) = ln(x)-ln(y)

$ln(3e^5)$ = ln(3) + $ln(e^5)$, since ln(xy) = ln(x) + ln(y)

$ln(\frac{3e^{5} }{x^3} )$ = ln(3) + $ln(e^5)-ln(x^3)$

$ln(\frac{3e^{5} }{x^3} )$ = $ln(3) + 5ln(e) -3ln(x)$, since ln($x^y$) = yln(x)

$ln(\frac{3e^{5} }{x^3} )$ = ln(3) + 5 -3ln(x) , since ln(e)=1

if needed further simplification,

ln(3) = 1.0986

ln(e) = 1

$ln(\frac{3e^{5} }{x^3} )$ = 6.0986 - 3ln(x)