# Thread: Logarithmic equation, please help!

1. ## Logarithmic equation, please help!

Please say me where I am wrong.... or show me how to continue to solve this equation...
Thanks

2. ## Re: Logarithmic equation, please help!

is the comma supposed to be a dot in $\displaystyle 2 lg^3 x - 1,5x$

3. ## Re: Logarithmic equation, please help!

isn't it the same? you can write it like that: $\displaystyle $$\left( {2{{\lg }^3}x - {3 \over 2}x} \right) \cdot \lg x = {1 \over 2}$$$

4. ## Re: Logarithmic equation, please help!

if I remember correctly, the log symbology lg indicates a base 2 logarithm ... ?

... your work shows you are assuming it's a base 10 logarithm.

5. ## Re: Logarithmic equation, please help!

in the country I live in, lg means log base 10, but I solved it already so no problem any more, it was a mistake in the textbook, there should be 1.5logx not just 1.5x

6. ## Re: Logarithmic equation, please help!

Getting back to the original equation, because you have the unknown, x, as base and in the exponent, there is not going to be any "algebraic" method. You might, with a lot of algebraic manipulation, get this into a form in which you could apply "Lambert's W function" (defined as the inverse function to $\displaystyle f(x)= xe^x$) but I don't see any simple way to do that.