simplify ln(1/(5e))

Solution

simplify

ln (\frac{1}{5 e})

- (ln (5) + 1)

Decimal Notation

- 2.60943 \dots

Solution steps

ln (\frac{1}{5 e})

Apply log rule:

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

ln (\frac{1}{5 e}) = ln (1) - ln (5 e)

= ln (1) - ln (5 e)

Apply log rule:

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

ln (5 e) = ln (5) + ln (e)

= ln (1) - (ln (5) + ln (e))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (5) + ln (e))

Apply log rule:

lo g_{a} (a) = 1

= 0 - (ln (5) + 1)

0 - (ln (5) + 1) = - (ln (5) + 1)

= - (ln (5) + 1)

\frac{1}{4} (ln (3 tan (\frac{x}{2} + 1)) - ln (tan (\frac{x}{2} + 3))) + c

0.423 - \frac{0.0592}{2} lo g_{10} (\frac{0.075}{0.1})

150 ln (\frac{350}{300})

ln (∣ cos (θ) 2 (ln ∣ 1 + cos (2 θ) ∣ - ln (2)))

ln (e^{3 x} \cdot sin (2 x))