If 4^a=8^b, find a/b

Answer 1

Take the logarithm of both sides: a*log(4) = b*log(8). Then rearrange: a/b = log(8)/log(4) = 1.5.

Answer 2

Hi Gabrielius T.

Use a common base where one exists.

4^a = 8^b

2 is a common base for 4 and 8

4 = 2²

8 = 2³

(2²)^a = (2³)^b

2^2a = 2^3b

2a = 3b

Divide both by b

2a/b = 3

Finally divide both sides by 2

a/b = 3/2 = 1.5

I hope this helps