Please could you explain how you converted the 8 into a 2 so that the two base numbers are the same?

Question

there was a tip in the question saying "Convert 8 to a power of 2" ... How did you do that? And is it the same method for all convertions? :o

Answer 1

Powers of 2:

2^ -3 = 1/8

2^ -2 = 1/4

2^ -1 = 1/2

2^ 0 = 1

2^ 1 = 2

2^ 2 = 4

2^ 3 = 8

So 8 expressed as a power of 2 is 2^3.

You could say the answer is 2^ (log(8) / log(2)), but since log(8)/log(2) = 3 it becomes 2^3

In general terms if you're asking for x expressed as a power of y, the answer will be y^ (log(y) / log(x)).

It's the same for all conversions if x and y are both positive numbers.