Question

If (2^a)=(3^b), what is the ratio of a to b?

Please use logarithms in the solution and explain.

Answer 1

Explanation:

Taking the log of both sides, we get:

a log 2 = b log 3

b log 3

Dividing both sides by log 2 yields a = ------------------

log 2

Finally, dividing both sides by b yields the desired ratio, a/b:

a log 3

---- = --------------

b log 2