If log_kx×log_5k=3, then x equals:

1958 AMC 12 Problem 25

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25.

\log_kx\cdot\log_5k=3,

then

x

equals:

k^6

5k^3

k^3

243

125

Use the chain identity

\log_kx\cdot\log_5k=\log_5x

Convert the resulting logarithmic equation to exponential form

By the change-of-base identity,

\log_kx\cdot\log_5k=\log_5x.

Hence

\log_5x=3,

x=5^3=125.

Thus, the correct answer is E.