Question

Ajutati-mă va rog frumos, exercițiul 02.

Answer 1

Salut,

$log_{\sqrt[3]2}(12\cdot\sqrt[3]{96})=\dfrac{log_2(12\cdot\sqrt[3]{96})}{log_2\sqrt[3]2}=\dfrac{log_2{12}+log_2\sqrt[3]{96}}{log_22^{\frac{1}3}}=\dfrac{log_2(4\cdot 3)+log_296^{\frac{1}3}}{\dfrac{1}3\cdot log_22}=\\\\=\dfrac{log_24+log_23+\dfrac{1}3\cdot log_2{96}}{\dfrac{1}3\cdot 1}=3\cdot\left[log_22^2+a+\dfrac{1}3\cdot log_2(3\cdot 32)\right]=\\\\=3\cdot 2\cdot log_22+3a+log_23+log_2(32)=6+3a+a+log_2(2^5)=\\\\=6+4a+5\cdot log_22=6+4a+5=11+4a.$

Green eyes.