Question

(5^(log5 (√3 + 8)) - 3^(log9 (√3 - 8)^2))^2

Answer 1

$\displaystyle (5^{log_5(\sqrt{3}+8)}-3^{log_9(\sqrt{3}-8)^2})^2=\\(5^{log_5(\sqrt{3}+8)}-3^{log_3(8-\sqrt{3})^{0,5*2}})^2=\\5^{log_5(\sqrt{3}+8)^2}-2*5^{log_5(\sqrt{3}+8)}*3^{log_3(8-\sqrt{3})}+3^{log_3(8-\sqrt{3})^2}=\\(\sqrt{3}+8)^2-2(\sqrt{3}+8)(8-\sqrt{3})+(8-\sqrt{3})^2=\\3+16\sqrt{3}+64-2(64-3)+3+64-16\sqrt{3}=\\67-122+67=12$

Answer 2

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