# Math Help - logarithm problem

1. ## logarithm problem

Hi,

I have a problem solving that equation logx sqrt 5 = -1/2 ... when i'm trying to solve I don't know what to do after I'm at that part of the equation x ^-1/2 = sqrt 5

Thanks for the help

Sebastien

2. ## Re: logarithm problem

Originally Posted by sebastien
Hi,

I have a problem solving that equation logx sqrt 5 = -1/2 ... when i'm trying to solve I don't know what to do after I'm at that part of the equation x ^-1/2 = sqrt 5

Thanks for the help

Sebastien
Hang on, is this \displaystyle \begin{align*} \log{(x)}\sqrt{5} = -\frac{1}{2} \end{align*} or \displaystyle \begin{align*} \log{(x\sqrt{5})} = -\frac{1}{2} \end{align*}?

Also, what is the base of the logarithm?

3. ## Re: logarithm problem

The equation is log base x sqrt 5 = -1/2

4. ## Re: logarithm problem

Originally Posted by sebastien
The equation is log base x sqrt 5 = -1/2
\displaystyle \begin{align*} \log_x{\sqrt{5}} &= -\frac{1}{2} \\ \sqrt{5} &= x^{-\frac{1}{2}} \\ 5 &= x^{-1} \\ 5^{-1} &= x \\ x &= \frac{1}{5} \end{align*}

5. ## Re: logarithm problem

thank you for the help