Question

Doar b...............​

Answer 1

$B = \dfrac{\log_{2}x+\log_{4}x+\log_{16}x}{\log_{5}x+\log_{25}x+\log_{0,2}x} \\\\ \\ B = \dfrac{\log_{2}x+\log_{2^2}x+\log_{2^4}x}{\log_{5}x+\log_{5^2}x+\log_{5^{-1}}x}\\ \\\\ B = \dfrac{\log_{2}x+\log_{2}{x^{\frac{1}{2}}}+\log_{2}x^{\frac{1}{4}}}{\log_{5}x+\log_{5}x^{\frac{1}{2}}+\log_{5}x^{-1}}\\ \\ \\ B = \dfrac{\log_{2}(x\cdot x^{\frac{1}{2}}\cdot x^{\frac{1}{4}})}{\log_{5}(x\cdot x^{\frac{1}{2}}\cdot x^{-1})}$

$\\B = \dfrac{\log_{2}x^{1+\frac{1}{2}+\frac{1}{4}}}{\log_{5}x^{1+\frac{1}{2}-1}} \\ \\ \\ B = \dfrac{\log_{2}x^{\frac{7}{4}}}{\log_{5}x^{\frac{1}{2}}}\\ \\ \\ B = \dfrac{\frac{7}{4}\cdot \log_{2}x}{\frac{1}{2}\cdot \log_{5}x}\\ \\ \\ B = \dfrac{7}{2}\cdot \log_{2}5\quad \checkmark$