Question

If (2^a)=(3^b), what is the ratio of a to b?
Please use logarithms in the solution and explain.

Answer 1

Answer:

Step-by-step 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