# Whether the statement, if x &gt; 0 and a &gt; 1 , then ln x ln a = ln x a is true or false. ### 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 11RQ
To determine

## Whether the statement, if x>0 and a>1, then lnxlna=lnxa is true or false.

Expert Solution

Solution:

The statement is false.

### Explanation of Solution

Let x=e3,a=e2.

Recall the logarithm rule, lnxm=mlnx.

Compute the value of lnx and lna as follows.

lnx=lne3=3lnelna=lne2=2lne

Thus, lnxlna=32.

Similarly, compute the value lnxa as follows.

lnxa=lne3e2=lne1=1

Therefore, lnxlnalnxa.

Therefore, the given statement is false.

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