simplify ln(aP^m)

Solution

simplify

ln (a P^{m})

ln (a) + m ln (P)

Solution steps

ln (a P^{m})

Apply log rule:

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

ln (a P^{m}) = ln (a) + ln (P^{m})

= ln (a) + ln (P^{m})

Apply log rule:

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

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

= ln (a) + m ln (P)

\frac{2 ln ( 3 ) - ln ( 5 )}{2 ln ( 5 )}

\frac{ln ( 7 ) - ln ( 10 )}{5.37}

- ln (1.5 \cdot 1 0^{- 3})

lo g_{10} (- 4 i)

0.065 \cdot ln (\frac{5}{150})