URGENTE!!
Dados log2= 0,301, log3= 0,477 e log7=0845, calcule.
A) Log ⁴√125
B) Log 25/6
C) Log 35
Soluções para a tarefa
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Letra A)
![\ell og(\sqrt[4]{125})~\Leftrightarrow~\ell og(\sqrt[4]{5^3})~\Leftrightarrow~\ell og(5^3)^{\frac{1}{4}}~\Leftrightarrow~\ell og(5)^{\frac{3}{4}}~\Leftrightarrow~ \frac{3}{4}\ell og(5)\\\\\frac{3}{4}\ell og(\frac{10}{2})~\Leftrightarrow~\frac{3}{4}(\ell og10-\ell og2)~\Leftrightarrow~\frac{3}{4}(1-0,301)~\Leftrightarrow~\frac{3}{4}(0,699)\\\\\dfrac{2,097}{4}~\Leftrightarrow~\fbox{$0,52425$}](https://tex.z-dn.net/?f=%5Cell+og%28%5Csqrt%5B4%5D%7B125%7D%29%7E%5CLeftrightarrow%7E%5Cell+og%28%5Csqrt%5B4%5D%7B5%5E3%7D%29%7E%5CLeftrightarrow%7E%5Cell+og%285%5E3%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7E%5CLeftrightarrow%7E%5Cell+og%285%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%7E%5CLeftrightarrow%7E+%5Cfrac%7B3%7D%7B4%7D%5Cell+og%285%29%5C%5C%5C%5C%5Cfrac%7B3%7D%7B4%7D%5Cell+og%28%5Cfrac%7B10%7D%7B2%7D%29%7E%5CLeftrightarrow%7E%5Cfrac%7B3%7D%7B4%7D%28%5Cell+og10-%5Cell+og2%29%7E%5CLeftrightarrow%7E%5Cfrac%7B3%7D%7B4%7D%281-0%2C301%29%7E%5CLeftrightarrow%7E%5Cfrac%7B3%7D%7B4%7D%280%2C699%29%5C%5C%5C%5C%5Cdfrac%7B2%2C097%7D%7B4%7D%7E%5CLeftrightarrow%7E%5Cfbox%7B%240%2C52425%24%7D+++ "\ell og(\sqrt[4]{125})~\Leftrightarrow~\ell og(\sqrt[4]{5^3})~\Leftrightarrow~\ell og(5^3)^{\frac{1}{4}}~\Leftrightarrow~\ell og(5)^{\frac{3}{4}}~\Leftrightarrow~ \frac{3}{4}\ell og(5)\\\\\frac{3}{4}\ell og(\frac{10}{2})~\Leftrightarrow~\frac{3}{4}(\ell og10-\ell og2)~\Leftrightarrow~\frac{3}{4}(1-0,301)~\Leftrightarrow~\frac{3}{4}(0,699)\\\\\dfrac{2,097}{4}~\Leftrightarrow~\fbox{$0,52425$}")
Letra B)
![\ell og(\frac{25}{6})~\Leftrightarrow~\ell og(25)-\ell og(6)~\Leftrightarrow~\ell og(5^2)-[\ell og(2\cdot3)]\\\\2\ell og(5)-[\ell og(2)+\ell og(3)]~\Leftrightarrow~2\ell og(\frac{10}{2})-[0,301+0,477]\\\\2\cdot[\ell og(10)-\ell og(2)]-[0,778]~\Leftrightarrow~2\cdot[1-0,301]-0.778\\\\2\cdot[0,699]-0,778~\Leftrightarrow~1,398-0,778~\Leftrightarrow~\fbox{$0,62$}](https://tex.z-dn.net/?f=%5Cell+og%28%5Cfrac%7B25%7D%7B6%7D%29%7E%5CLeftrightarrow%7E%5Cell+og%2825%29-%5Cell+og%286%29%7E%5CLeftrightarrow%7E%5Cell+og%285%5E2%29-%5B%5Cell+og%282%5Ccdot3%29%5D%5C%5C%5C%5C2%5Cell+og%285%29-%5B%5Cell+og%282%29%2B%5Cell+og%283%29%5D%7E%5CLeftrightarrow%7E2%5Cell+og%28%5Cfrac%7B10%7D%7B2%7D%29-%5B0%2C301%2B0%2C477%5D%5C%5C%5C%5C2%5Ccdot%5B%5Cell+og%2810%29-%5Cell+og%282%29%5D-%5B0%2C778%5D%7E%5CLeftrightarrow%7E2%5Ccdot%5B1-0%2C301%5D-0.778%5C%5C%5C%5C2%5Ccdot%5B0%2C699%5D-0%2C778%7E%5CLeftrightarrow%7E1%2C398-0%2C778%7E%5CLeftrightarrow%7E%5Cfbox%7B%240%2C62%24%7D "\ell og(\frac{25}{6})~\Leftrightarrow~\ell og(25)-\ell og(6)~\Leftrightarrow~\ell og(5^2)-[\ell og(2\cdot3)]\\\\2\ell og(5)-[\ell og(2)+\ell og(3)]~\Leftrightarrow~2\ell og(\frac{10}{2})-[0,301+0,477]\\\\2\cdot[\ell og(10)-\ell og(2)]-[0,778]~\Leftrightarrow~2\cdot[1-0,301]-0.778\\\\2\cdot[0,699]-0,778~\Leftrightarrow~1,398-0,778~\Leftrightarrow~\fbox{$0,62$}")
Letra C)
![\ell og(35)~\Leftrightarrow~\ell og(7\cdot5)~\Leftrightarrow~\ell og(7)+\ell og(5)~\Leftrightarrow~0,845+\ell og(\frac{10}{2})\\\\0,845+[\ell og(10)-\ellog(2)]~\Leftrightarrow~0,845+[1-0,301]~\Leftrightarrow~0,845+0,699\\\\\fbox{$1,544$}](https://tex.z-dn.net/?f=%5Cell+og%2835%29%7E%5CLeftrightarrow%7E%5Cell+og%287%5Ccdot5%29%7E%5CLeftrightarrow%7E%5Cell+og%287%29%2B%5Cell+og%285%29%7E%5CLeftrightarrow%7E0%2C845%2B%5Cell+og%28%5Cfrac%7B10%7D%7B2%7D%29%5C%5C%5C%5C0%2C845%2B%5B%5Cell+og%2810%29-%5Cellog%282%29%5D%7E%5CLeftrightarrow%7E0%2C845%2B%5B1-0%2C301%5D%7E%5CLeftrightarrow%7E0%2C845%2B0%2C699%5C%5C%5C%5C%5Cfbox%7B%241%2C544%24%7D "\ell og(35)~\Leftrightarrow~\ell og(7\cdot5)~\Leftrightarrow~\ell og(7)+\ell og(5)~\Leftrightarrow~0,845+\ell og(\frac{10}{2})\\\\0,845+[\ell og(10)-\ellog(2)]~\Leftrightarrow~0,845+[1-0,301]~\Leftrightarrow~0,845+0,699\\\\\fbox{$1,544$}")
Letra B)
Letra C)
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