Problem: If a=8225a=\log _{\mathrm{8}} 225a=log8​225 and b=215\mathrm{b}=\log _{2} 15b=log2​15, then a‾\underline{a}a​, in terms of b‾\underline{b}b​, is:
Answer Choices:
A. b/2\mathrm{b} / 2b/2
B. 2b/32 b / 32b/3
C. bbb
D. 3 b/23 \mathrm{~b} / 23 b/2
E. 2 b Solution:
Since a=8225,8a=225,23a=152a=\log _{8} 225,8^{a}=225,2^{3a}=15^{2}a=log8​225,8a=225,23a=152 \quad
b=215,2b=15,22b=152b=\log _{2} 15,2^{b}=15,2^{2 b}=15^{2}b=log2​15,2b=15,22b=152 \quad
∴23a=22b,3a=2b,a=2b3\therefore 2^{3a}=2^{2 b}, 3 a=2 b, a=\dfrac{2 b}{3}∴23a=22b,3a=2b,a=32b​ \quad