Use the Laws of Logarithms to combine ech expression into a single logarithm. NS

melodykap

melodykap

Answered question

2021-10-16

Use the Laws of Logarithms to combine ech expression into a single logarithm.
(a) 3logx+12log(x+1)
(b) 3logs+12lnt4ln(t2+1)

Answer & Explanation

sweererlirumeX

sweererlirumeX

Skilled2021-10-17Added 91 answers

Step 1
Apply Laws of Logarithms to combine expression into single logarithm.
a) 3logx+12log(x+1)
Apply logarithms Law: bloga=logab
3logx+12log(x+1)=logx3+log(x+1)12
=logx3+logx+1
Apply logarithms Law: loga+logb=log(ab)
3logx+12log(x+1)=logx3+logx+1
=log(x3x+1)
Step2
(b) 3lns+12lnt4ln(t2+1)
Apply logarithms Law: blna=lnab 3lns+12lnt4ln(t2+1)=lns3+lntln(t2+1)4
Apply logarithms Law: lna+lnb=ln(ab)  and  lnalnb=ln(ab)
3lns+12lnt4ln(t2+1)=lns3+lntln(t2+1)4
=ln(s3t)ln(t2+1)4
=ln(s3t(t2+1)4)
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-03Added 2605 answers

Answer is given below (on video)

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