simplify ln((2e)/3)

Solution

simplify

ln (\frac{2 e}{3})

ln (2) + 1 - ln (3)

Decimal Notation

0.59453 \dots

Solution steps

ln (\frac{2 e}{3})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2 e}{3}) = ln (2 e) - ln (3)

= ln (2 e) - ln (3)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 e) = ln (2) + ln (e)

= ln (2) + ln (e) - ln (3)

Apply log rule:

lo g_{a} (a) = 1

= ln (2) + 1 - ln (3)

- lo g_{10} (5.2 \cdot 1 0^{- 4})

\frac{ln ( 37 ) + 2 ln ( 4 )}{ln ( 4 )}

ln (\frac{e ^{2 x} cos ( 3 x )}{x - 4})

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ln (\frac{tan ( x )}{2})