# The equation, ln ( ln x ) = 1 for x .

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

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

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 .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!