How do you expand #Ln[(5e4sqrtt^5)/(am)] #?

1 Answer
Jul 6, 2017

Answer:

#ln[frac{5e4sqrtt^5}{am}]#
# = ln20 + 1 + 5/2lnt - lna - lnm#

Explanation:

#ln[frac{5e4sqrtt^5}{am}]#

Rewrite the numerator:
# = ln[ frac{20et^(5/2)}{am} ]#

Separate numerator and denominator:
# = ln(20et^(5/2)) - ln(am)#

Expand each natural log using the logarithm rule of products:
# = [ln20 + color(blue)(lne) + ln(t^(5/2))] - [ln a + ln m]#

#color(blue)("Note that "lne=1)#

# = ln20 + 1 + 5/2lnt - lna - lnm#