\text{Use the properties of logarithms, given that }\ln(2) - 0.6931\text{ and

enfurezca3x

enfurezca3x

Answered question

2021-11-16

Use the properties of logarithms, given that  ln(2)0.6931  and  ln(3)1.0986,  to approximate the logarithm. Use a calculator to confirm your approximations.
(a)  ln(0.75)=
(b)  ln(54)=
(c)  ln(312)=
(d)  ln(172)=

Answer & Explanation

Marian Tucker

Marian Tucker

Beginner2021-11-17Added 15 answers

Step 1
Properties of logarithms :
ln(a×b)=ln(a)+ln(b)
ln(ab)=ln(a)ln(b)
ln(an)=nln(a)
Step 2
given  ln(2)0.6931  and  ln(3)
=1.0986
a)  ln(0.75)
Answer:  
ln(0.75)=ln(34)
=ln(3)ln(4)  [lnab=lnalnb]
=ln(3)2ln(2)
=1.0986(0.6931)2
[ln(0.75)=0.2876]
b)  ln54
Answer:
ln(54)=ln(9×6)
=ln(9)+ln(6)
=ln(32)+ln(3×2)
=2ln(3)+ln(3)+ln(2)
=3ln(3)+ln(2)
ln(54)=3(1.0986)+0.6931
[ln(54)=3.9889]
Opeance1951

Opeance1951

Beginner2021-11-18Added 26 answers

c)  ln(312)
Answer:  
ln(312)=ln(12)13  [lnxn=nlnx]
=13ln(12)
=13ln(4×3)  [lnab=lna+lnb]
=13[ln(4)+ln(3)]
=13[2ln(2)+ln(3)]
=13[2(0.6931)+1.0986]
[ln(312)=0.8283]
user_27qwe

user_27qwe

Skilled2021-11-24Added 375 answers

 d)ln(172)=ln(72)  [ln(1a)=ln(a)]
=ln(23×32)
=[3ln(2)+2ln(3)]
=3×(0.6931)2×(1.0986)
[ln(172)=4.2765]

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?