[tex]log_4 \sqrt{2} + log_4 3 = log_4 3\sqrt{2} \\ \\ 16 = 4^2 \\ \\ (4^2)^{log_4 3\sqrt{2}} = 4^{2log_4 3\sqrt{2}} = 4^{log_4 (3\sqrt{2})^2}} = 4^{log_4 18} = 18 [/tex]
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16^(log₄ √2 + log₄ 3) = (4²)^[log₄ (√2 * 3] = 4^(2 * log₄ 3√2) = 4^log₄ (3√2)² = 4^log₄ 18 = 18
