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 $\lg_{1.5}{n}$?