Mathematics, 22.07.2019 16:30 richy5667
Find log_{3} [27*\sqrt[4]{3} ] wihout using a calculator. show all work!
Answers: 1
![\bf \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y)\\\\ -------------------------------\\\\ log_3(27\sqrt[3]{3})\qquad \begin{cases} 27=3\cdot 3\cdot 3\\ \qquad 3^3\\ \sqrt[3]{3}=\sqrt[3]{3^1}\\ \qquad 3^{\frac{1}{3}} \end{cases}\implies log_3\left( 3^3\cdot 3^{\frac{1}{3}} \right) \\\\\\ log_3\left( 3^{3+\frac{1}{3}} \right)\implies log_3\left( 3^{\frac{4}{3}} \right)\implies \cfrac{4}{3}\cdot log_3(3)\implies \cfrac{4}{3}\cdot 1\implies \cfrac{4}{3}](/tpl/images/0120/2026/603a3.png)
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Find log_{3} [27*\sqrt[4]{3} ] wihout using a calculator. show all work!...
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