If In a = 2, In b = 3, and In c = 5, evaluate the following: %3| %3| a (a) In (b) In Va*b°cª 413 4 ||

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If In a = 2, In b = 3, and In c =
5, evaluate the following:
4
(a) In
63 c2
(b) In Vab®c4
Transcribed Image Text:If In a = 2, In b = 3, and In c = 5, evaluate the following: 4 (a) In 63 c2 (b) In Vab®c4
Expert Solution
Step 1

GIVEN DATA : The value of ln a=2, ln b=3 and ln c=5

       TO FIND : Evaluate 

(a). lna4b3c2

(b). lna4b3c4

Step 2

(a). Given expression lna4b3c2

Apply quotient rule of logarithm : logmab=logma-logmb

lna4b3c2=lna4-lnb3c2

Apply product rule of logarithm: lnm(ab)=lnm(a)+lnm(b)

lna4b3c2=lna4-lnb3+ln(c2)

lna4b3c2=lna4-lnb3-ln(c2)

Apply power rule of logarithm : lnm(ak)=k( lnma)

lna4b3c2=4lna-3lnb-2ln(c)

 

Step 3

Substitute the values of ln a=2, ln b=3 and ln c=5 from the given data

lna4b3c2=4(2)-3(3)-2(5)

lna4b3c2=8-9-10

ln(a4b3c2)=(-11)

Step 4

(b). The given expression is lna4b3c4

Apply the exponent rule of power of power : (xa)b=xab

lna4b3c4=lna22b2bc22

Square root is expressed as : x=x2

lna4b3c4=lna2bc2b

lna4b3c4=lna2c2bb

lna4b3c4=lna2c2bb12

Apply the multiplication rule of exponent : xa×xb=xa+b

lna4b3c4=lna2c2b32

 

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