Exercise 16 Page 481

To write the given expression as a single natural logarithm, we will use three Properties of Logarithms. Note that these properties also apply for natural logarithms, since a natural logarithm is just a logarithm with base e. For example, in our case log_e x = ln x. Power Property:& n ln m = ln m^n Quotient Property:& ln m - ln n = ln mn Product Property:& ln m + ln n = ln mn Let's apply the above properties to our expression!

ln a - 2 ln b + 1/3 ln c

b*ln(a)=ln(a^b)

ln a - ln b^2 + ln c^(13)

PowToRootD

a^(1n)=sqrt(a)

ln a - ln b^2 + ln sqrt(c)

log(m) - log(n)=log(m/n)

ln a/b^2 + ln sqrt(c)

log(m) + log(n)=log(mn)

ln ( a/b^2sqrt(c) )