Simple Logarithmic Equation Clarification.

• Sep 21st 2010, 01:10 AM
BinaryBoy
Simple Logarithmic Equation Clarification.
Hi all,

Just another logarithmic question here. I need to solve logx (3) = 1/2 for x and I am not sure why the answer is 9. I think it has something to do with square roots, but I am not confident of the logical order in which that would appear.

From the above I gather that x is the base, 1/2 is the power, and 3 is the numeral found.

So:

x (to the power of 1/2) = 3.

I am just not sure why one would have to square root 9.

Sorry if it is a silly question. Any help much appreciated!

Thanks,

Nathaniel
• Sep 21st 2010, 01:18 AM
MathoMan
$x^{\frac{1}{2}}=\sqrt{x}$. Generally, $x^{\frac{1}{n}}=\sqrt[n]{x}$.
So you have $\sqrt{x}=3.$ Square the equation and there you have it: 9.
• Sep 21st 2010, 01:20 AM
mr fantastic
Quote:

Originally Posted by BinaryBoy
Hi all,

Just another logarithmic question here. I need to solve logx (3) = 1/2 for x and I am not sure why the answer is 9. I think it has something to do with square roots, but I am not confident of the logical order in which that would appear.

From the above I gather that x is the base, 1/2 is the power, and 3 is the numeral found.

So:

x (to the power of 1/2) = 3.

I am just not sure why one would have to square root 9.

Sorry if it is a silly question. Any help much appreciated!

Thanks,

Nathaniel

By definition $\displaystyle \log_A B = C \Leftrightarrow A^C = B$.

Therefore $\displaystyle \log_x 3 = \frac{1}{2} \Leftrightarrow x^{1/2} = 3$.

Square both sides to get x.
• Sep 21st 2010, 02:06 AM
BinaryBoy
That was a huge help MathoMan and Mr Fantastic. I guess I just have to really know and understand those basic logarithmic rules.

Thanks!!!