Question

s=log6
36 + log 10 0,01 - log 1/4 2 raiz quadrada de 2

me ajuda pfv

Answer 1

$S=\log_6 36 + \log_{10} 0,01 - log_{\frac{1}{4}} 2 \sqrt{2} \\ \\ S=2-2- \log_{2^{-2}} 2\cdot2^{\frac{1}{2}} \\ \\ S=0- \log_{2^{-2}} 2^{1+\frac{1}{2}} \\ \\ S=- \log_{2^{-2}} 2^{\frac{3}{2}} \\ \\ S=-(-\frac{3}{4}) \\ \\ S=\frac{3}{4}$

Na quarta linha, pode ser interpretado assim:

$\log_{2^{-2}} 2^{\frac{3}{2}} \\ \\ (2^{-2})^x=2^{\frac{3}{2}} \\ \\ 2^{-2x}=2^{\frac{3}{2}} \\ \\ -2x=\frac{3}{2} \\ \\ x=-\frac{3}{4}$