Найдите значение выражения (2log49 12/7 - log7 12 + 9) * 4^3log4 2.5. Created by bullet15102000p1h7kn. algebra-ru

7 - log7 12 + 9) * 4^3log4 2.5...

bullet15102000p1h7kn @bullet15102000p1h7kn

September 2021 2 1 Report

Найдите значение выражения
(2log49 12/7 - log7 12 + 9) * 4^3log4 2.5

mukus13

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$(2log_{49} \frac{12}{7} - log_7 12 + 9) * 4^{3log_4 2.5}=(2log_{7^2} \frac{12}{7} - log_7 12 + 9) * 4^{3log_4 2.5}=$ $=(2* \frac{1}{2} log_{7} \frac{12}{7} - log_7 12 + 9) * 4^{3log_4 2.5}=$ $=(log_{7} (\frac{12}{7}: 12) + 9) * 4^{3log_4 \frac{5}{2} }=(log_{7} (\frac{12}{7}* \frac{1}{12} ) + 9) * 4^{log_4 (\frac{5}{2})^3 }=$ $=(log_{7} \frac{1}{7} + 9) * 4^{log_4 \frac{125}{8} }=(log_{7}7^{-1} + 9) * 4^{log_4 \frac{125}{8} }=$ $=(-1 + 9) * 4^{log_4 \frac{125}{8} }=8 * \frac{125}{8} }=125$

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