2025 AMC 12B Problems/Problem 1

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Problem

What is the value of $\log_2({1+\sqrt{2}+\sqrt{3}})+\log_2({1+\sqrt{2}-\sqrt{3}})$?

$\textbf{(A)}~1\qquad\textbf{(B)}~\frac{3}{2}\qquad\textbf{(C)}~2\qquad\textbf{(D)}~\frac{5}{2}\qquad\textbf{(E)}~3$

Solution

See also

2025 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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