# Simple Evaluating Logarithmics

• Dec 9th 2007, 04:13 PM
Macleef
Simple Evaluating Logarithmics
Is $\displaystyle logx$ defined for $\displaystyle x = 0$?

No, because x > 0. Is this correct?

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Evaluate:

1) $\displaystyle log( \frac {1}{10^2} )$

$\displaystyle -2$?

2) $\displaystyle log_3 \sqrt3$

$\displaystyle - \frac {1}{3}$ ?

3) $\displaystyle log_93$

$\displaystyle \sqrt3$ ?

Can you please check to see if I did the questions correctly?

• Dec 9th 2007, 04:22 PM
Jhevon
Quote:

Originally Posted by Macleef
Is $\displaystyle logx$ defined for $\displaystyle x = 0$?

No, because x > 0. Is this correct?

the domain of the logarithm is x > 0. because there is no power we can raise a number to to get 0

Quote:

Evaluate:

1) $\displaystyle log( \frac {1}{10^2} )$

$\displaystyle -2$?
correct

Quote:

2) $\displaystyle log_3 \sqrt3$

$\displaystyle - \frac {1}{3}$ ?
wrong. what is $\displaystyle \sqrt{3}$ written as 3 to some power?

Quote:

3) $\displaystyle log_93$

$\displaystyle \sqrt3$ ?

wrong. what power do we have to raise 9 to to get 3?
• Dec 9th 2007, 04:28 PM
Macleef
Quote:

Originally Posted by Jhevon
the domain of the logarithm is x > 0. because there is no power we can raise a number to to get 0

correct

wrong. what is $\displaystyle \sqrt{3}$ written as 3 to some power?

wrong. what power do we have to raise 9 to to get 3?

2) $\displaystyle \frac {1}{2}?$

3) $\displaystyle \frac {1}{2}?$
• Dec 9th 2007, 04:37 PM
Jhevon
Quote:

Originally Posted by Macleef
2) $\displaystyle \frac {1}{2}?$

3) $\displaystyle \frac {1}{2}?$