1953 AMC 12 Problem 5

Attempt Problem 5 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

If log⁡6x=2.5,\log_6 x=2.5, the value of xx is:
9090
3636
36636\sqrt6
0.50.5
none of these
Answer: C
Concepts:logarithmsfractional exponentsradicals
Small hint:
Rewrite the logarithmic equation in exponential form
Big hint:
Use 2.5=2+122.5=2+\tfrac12
Solution:
The equation gives x=62.5=626=366. x=6^{2.5}=6^2\sqrt6=36\sqrt6.
Thus, the correct answer is C.
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