BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.6, Problem 52E

(a)

To determine

To solve: The equation, ln(lnx)=1 for x.

Expert Solution

Answer to Problem 52E

The value of x=ee .

Explanation of Solution

The given equation is ln(lnx)=1 .

Taking natural exponential on both sides, eln(lnx)=e1

Use the law of logarithm, elnx=x,x>0 and obtain, lnx=e .

Again taking natural exponential on both sides, elnx=ee .

Again apply the law of logarithm, elnx=x,x>0 and obtain, x=ee .

Thus, the value of x=ee .

(b)

To determine

To solve: The equation, eax=Cebx,ab for x.

Expert Solution

Answer to Problem 52E

The values of x=lncab .

Explanation of Solution

The given equation is eax=Cebx,ab .

Simplify the given equation as follows.

eax=Cebxeaxebx=Ce(ab)x=C

Taking natural log on both sides, lne(ab)x=lnc .

Use the law of logarithm, ln(ex)=x,x and simplify further as follows.

(ab)x=lncx=lncab

Thus, the values of x=lncab .

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