Answer:
ln(108) = 3.58
Step-by-step explanation:
Data provided:
ln(2) ≈ 0.69
and
ln(3) ≈ 1.10
equation to be solved
ln(108)
now,
ln(108) = ln (2 × 54)
or
= ln( 2 × 2 × 27 )
or
= ln( 2 × 2 × 3 × 3 × 3 )
or
= ln( 2² × 3³ )
Now,
we have the property of log function as:
1) ln(AB) = ln(A) + ln(B)
and,
2) ln(xⁿ) = n × ln(x)
on applying the above properties , we get
ln( 2² × 3³ ) = ln(2²) + ln(3³) using property (1)
or
= 2ln(2) + 3ln(3) using property (2)
on substituting the values given in the question
we get
ln(108) = ( 2 × 0.69 ) + ( 2 × 1.10 )
= 1.38 + 2.20
= 3.58
