Write the following as a single logarithm Write the followin

Write the following as a single logarithm:

Write the following as a single logarithm: 2 ln 4 + ln 3 - ln 8

Solution

2ln4 + ln3 - ln8

==> 2ln2² + ln3 - ln2³

==> 2(2)ln2 + ln3 - (3)ln2       since ln a^b = blna

==> 4ln2 - 3ln2 + ln3

==> ln2 + ln3

==> ln[(2)(3)]     since ln a + ln b = ln (ab)

==> ln6

Hence 2ln4 + ln3 - ln8 = ln6