simplify ln(2(e^e))

Solution

simplify

ln (2 (e^{e}))

ln (2) + e

Decimal Notation

3.41142 \dots

Solution steps

ln (2 (e^{e}))

Apply log rule:

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

ln (2 (e^{e})) = ln (2) + ln (e^{e})

= ln (2) + ln (e^{e})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{e}) = e ln (e)

= ln (2) + e ln (e)

e ln (e) = e

= ln (2) + e

3 lo g_{10} (a) + lo g_{10} (b) - \frac{1}{2} lo g_{10} (c)

\frac{1}{5} lo g_{8} (3)

lo g_{10} (x^{3}) - lo g_{10} (y^{4}) + lo g_{10} (z)

ln (\frac{1 + 0.65}{365})