Expert: Paul Klarreich - 2/26/2007

Question
HEy can you help me solve this one:
"if 2 raised to 6.5 = a
  3 raised to 7.5 = b
  what is 6 raised to 9.5 equal to in terms of a and b. thanks"


Answer
Questioner:   Leonard
Category:  Advanced Math
 
Subject:  algebra-exponent
Question:  HEy can you help me solve this one:
"if 2 raised to 6.5 = a
 3 raised to 7.5 = b
 what is 6 raised to 9.5 equal to in terms of a and b. thanks"
......................................
Hi, Leonard,

(Note: This is a high class web site, and the word 'Hey' is not used here.)

If  a = 2^6.5 = 2^(13/2),  then  2 = a^2/13
If  b = 3^7.5 = 3^(15/2),  then  3 = b^2/15

6^9.5 = (3*2)^9.5 =  3^9.5  2^9.5 = 3^(19/2) 2^(19/2)

= (b^2/15)^19/2 (a^2/13)^19/2

= b^19/15 a^19/13

Sorry I can't do better than that.