Question

Calculati: ...............




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Answer 1

$\it log_3\dfrac{1}{2187} =log_33^{-7}=-7log_3 3 = -7\\ \\ \\ log_5\dfrac{1}{125}=log_5 5^{-3}=-3log_5 5=-3\\ \\ \\ log_9\sqrt[3]{3}=log_9 3^{\frac{1}{3}}=log_9 (3^2)^{\frac{1}{6}}=log_9 9^{\frac{1}{6}}=\dfrac{1}{6}log_9 9=\dfrac{1}{6}\\ \\ \\ log_3 \Big(log_{\frac{1}{2}}\ \dfrac{1}{512}\Big)=log_3\Big(log_{\frac{1}{2}}(\dfrac{1}{2})^{9}\Big)=log_3 9=2$

$\it log_35+log_3 16,5=log_3 5\cdot 16,2=log_3 81=log_3 3^4=4$

$\it lg\dfrac{1}{100}=lg10^{-2}=-2lg10=-2\cdot1=-2\\ \\ \\ ln\dfrac{1}{e^7}=ln e^{-7}=-7\cdot ln e=-7\cdot1=-7\\ \\ \\ log_{12}288-log_{12}2=log_{12}(288:2)=log_{12}144=log_{12} 12^2=2\cdot log_{12} 12=2$