Thread: Write as a single logarithm.

1. Write as a single logarithm.

3log2x + 1/2log2x - 2log2(x+1)

I don't quite understand this. Ive gotten to "log2 x^3(x^1/2)/(x+1)^2"
Any help would be great.
Thanks.

~freak

2. Joining logs

$\displaystyle 3log2x + (1/2)log2x - 2log2(x+1)$

=$\displaystyle log(2x)^3 + log(2x)^{1/2} - log{(2(x+1))}^2$

=$\displaystyle log(2x)^{3.5} - log{(2(x+1))}^2$

=$\displaystyle log \frac{(2x)^{3.5}}{{(2(x+1))}^2}$

3. Thanks, i looked it over again and realized where i went wrong. I got the same asnwer as you did but the book had the top x to the power of 7/2. It took me to right after i posted this to realized that 3.5 and 7/2 were the same thing lol.
Thanks for the help.

~freak