So for each of these images, I need to divide them four times, so that they are 4 times nested within the largest image. I understand that part.
a) For the first figure (the L-shaped figure), how many tiles are there of the smallest size after 10 divisions?
b) again for the first figure, how many total tiles are there after 10 divisions.
My attempt:
a) $4^x = 10$
$x\log _{10} 4 = \log _{10} 10$
$x\log_{10} 4 = 1$
$x = \frac{1}{\log_{10}4}$
b) $\frac{1-4^{n+1}}{1-4} = 10$
$(1-4^{n+1}) = -30$
Don't know where to go from here
a) If I understand it correctly, one division is dividing the tile into four parts. So you need to perform division of all tiles 10 times. i.e. You start with one tile, you divide it to 4, then you divide the 4 into 16 etc.... $$4^{10} = 1048576$$
b) I think, they didn't formulate it well. I assume, one divided tile also counts as a tile. It is then: $$1 + 4 + 4^2 + 4^3 + 4^4 + 4^5 +4^6 + 4^7 + 4^8 + 4^9 + 4^{10} = 1398101$$