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

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Answer 1 · 2017-07-06T15:42:31

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

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

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:
$= [ln20 + color(blue)(lne) + ln(t^(5/2))] - [ln a + ln m]$

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

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

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