2015 AMC 12B Problem 8 — Solution | LIVE by Po-Shen Loh

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2015 AMC 12B Problem 8

Attempt Problem 8 of the 2015 AMC 12B 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 2015 AMC 12B solutions, or check the answer key.

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

8.

What is the value of $\left(625^{\log_5 2015}\right)^{\frac14}?$

$5$

$\sqrt[4]{2015}$

$625$

$2015$

$\sqrt[4]{5^{2015}}$

Answer: D

Concepts:logarithm exponent

Difficulty rating: 1460

Solution:

Since $625 = 5^4,$ we have $\begin{gathered} 625^{\log_5 2015} = 5^{4\log_5 2015} \\ = \left(5^{\log_5 2015}\right)^4 = 2015^4. \end{gathered}$

Taking the fourth root gives $\left(2015^4\right)^{1/4} = 2015.$

Thus, the correct answer is D.

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