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Problem 422

AMC 12 late, AIME early

Algebra Difficulty 4.8 Find the answer

$1 \cdot 28$ Calculate $7^{\log 49^{5}}-0.5$ .

Translate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

[Solution] $7^{\log 49^{5}}-0.5=\frac{7^{\log 49^{5}}}{7^{0.5}}=\frac{7^{\log _{7} 5}}{\sqrt{7}}=\frac{\sqrt{5}}{\sqrt{7}}=\frac{1}{7} \sqrt{35}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.