Suppose that ln 2 a and ln 5 b use properties of logarithm

Suppose that ln 2 = a and ln 5 = b. use properties of logarithms to write the given logarithm in terms of a and b. a) ln 20

Solution

ln 20= ln(4*5)

=ln (4) + ln (5) {since ln(x*y)= ln(x)+ln(y)}

=ln( 2²) +ln(5) {since 4= 2²}

= 2 ln(2) + ln(5) {since ln mⁿ= n ln(m)}

=2a+b

Hence ln 20= 2a+b