Question

log(3) 2×log(7)5×log(2)3×log(5)7
log(2)√2
log(√2)2

Answer 1

$\displaystyle\bf\\1)\\\\\log_{3} 2\cdot \log_{7}5\cdot \log_{2} 3\cdot\log_{5} 7=\\\\\\=\underbrace{\log_{3} 2\cdot \log_{2}3}_{1}\cdot \underbrace{\log_{7} 5\cdot\log_{5} 7}_{1}=1\cdot 1=1\\\\2)\\\\\log_{2} \sqrt{2} =\log_{2} 2^{\frac{1}{2 } }=\frac{1}{2} \log_{2} 2=\\\\\\=\frac{1}{2} \cdot 1=\frac{1}{2} =0,5\\\\3)\\\\\log_{\sqrt{2} } 2=\log_{(\sqrt{2} )^{2} } 2^{2} =\log_{2} 4=\\\\\\=\log_{2} 2^{2} =2\log_{2} 2=2$