MATH SOLVE

4 months ago

Q:
# Use logarithmic properties and the fact that ln(2) ≈ 0.69 and ln(3) ≈ 1.10 to approximate the value of each of thefollowing logarithmic expressions. Do not use a calculator. ln(108)

Accepted Solution

A:

Answer:ln(108) = 3.58Step-by-step explanation:Data provided:ln(2) ≈ 0.69and ln(3) ≈ 1.10equation to be solvedln(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 getln( 2² × 3³ ) = ln(2²) + ln(3³) using property (1)or= 2ln(2) + 3ln(3) using property (2)on substituting the values given in the questionwe getln(108) = ( 2 × 0.69 ) + ( 2 × 1.10 )= 1.38 + 2.20= 3.58