simplify ln(ce^c)

Solution

simplify

ln (c e^{c})

ln (c) + c

Solution steps

ln (c e^{c})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (c) + c ln (e)

c ln (e) = c

= ln (c) + c

- lo g_{10} (8.83 \cdot 1 0^{- 3})

ln ((2 e^{b d} cosh (b u h) + 1)^{N})

ln (\frac{1}{81})

0.5 ln (100) - 2 ln (x) + 8 ln (y)

ln (\frac{1}{0.5}) - e^{- x^{3}}