simplify ln(6e^m)

Solution

simplify

ln (6 e^{m})

ln (6) + m

Solution steps

ln (6 e^{m})

Apply log rule:

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

ln (6 e^{m}) = ln (6) + ln (e^{m})

= ln (6) + ln (e^{m})

Apply log rule:

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

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

= ln (6) + m ln (e)

m ln (e) = m

= ln (6) + m

- \frac{1}{2} ln (\frac{1}{16}) + ln (\frac{1}{2})

ln (x^{4} y^{3})

(\frac{1}{0.143}) ln (\frac{5 x 1 0 ^{9}}{34000})

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

lo g_{a} (5) + 2 lo g_{a} (x) + 4 lo g_{a} (y^{3})