Problem: If kx⋅5k=3\log _{k} x \cdot \log _{5} k=3logk​x⋅log5​k=3, then xxx equals:
Answer Choices:
A. k5\mathrm{k}^{5}k5
B. 5k35 \mathrm{k}^{3}5k3
C. k3\mathrm{k}^{3}k3
D. 243243243
E. 125125125 Solution:
A=kxB=5kA=\log _{k} x \qquad B=\log _{5} k A=logk​xB=log5​k
x=kAk=5Bx=k^{A} \qquad k=5^{B} x=kAk=5B
(kx)(5k)=AB=3\left(\log _{k} x\right)\left(\log _{5} k\right)=A B=3 (logk​x)(log5​k)=AB=3
x=(5B)A=53=125x=\left(5^{B}\right)^{A}=5^{3}=125 x=(5B)A=53=125