I am asking another question at StackOverflow about Big-O
On 1st line is something like
The size of the problem at level k is (2/3)kn. The size at the lowest level is 1, so setting (2/3)kn = 1, the depth is k = log1.5 n (divide both sides by (2/3)k, take logs base 1.5).
the main question is I have
$1 = \left(\frac{2}{3}\right)^k \cdot n$
I want to find k. I did
$\left(\frac{2}{3}\right)^k n=1$ $\left(\frac{2}{3}\right)^k=\frac{1}{n}$ $k\lg\frac{2}{3}=\lg\frac{1}{n}$ $k=\frac{\lg\frac{1}{n}}{\lg\frac{2}{3}}$ $k=\lg_{\frac{2}{3}}\frac{1}{n}$
I suppose I could somehow convert it to the desired answer $\lg_{1.5}{n}$?