# ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) ... ( log 31 32 ) .

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 1, Problem 11P
To determine

## To evaluate: (log23)(log34)(log45)...(log3132).

Expert Solution

Solution:

The value of the expression is 5.

### Explanation of Solution

Given:

(log23)(log34)(log45)...(log3132)

Result used:

logab=logbloga

logxn=nlogx

Calculation:

Apply the result in the given expression,

(log23)(log34)(log45)...(log3132)=log3log2log4log3log5log4log6log5...log31log30log32log31 =log32log2=log25log2=5log2log2

Simplify further, (log23)(log34)(log45)...(log3132)=5

Thus, the value of the expression is 5.

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