Problem: If a=8225a=\log _{8} 225a=log8225 and b=215b=\log _{2} 15b=log215, then
Answer Choices:
A. a=12ba=\dfrac{1}{2} ba=21b B. a=23ba=\dfrac{2}{3} ba=32b C. a=ba=ba=b D. b=12ab=\dfrac{1}{2} ab=21a E. a=32ba=\dfrac{3}{2} ba=23b
Solution:
225=8a=23a∴15=23a/2225=8^{a}=2^{3 a} \therefore 15=2^{3 a / 2}225=8a=23a∴15=23a/2. Also 15=2b∴3a/2=b∴a=2b/315=2^{b} \quad \therefore 3 a / 2=b \quad \therefore a=2 b / 315=2b∴3a/2=b∴a=2b/3.