Question

Log de 9 na base √3 + log de 125 na base 0,04 + log de √32 na base 2

Answer 1

$log9_{\sqrt{3}} \\ \sqrt{3}^{x} = 9\\ (\sqrt{3}^{x})^{2} = 9^{2}\\ 3^{x} = 81\\ 3^{x} = 3^{4} \\ x = 4$

$log\sqrt{32}_{2 } \\ 2^{x} = \sqrt{32}\\ (2^{x})^{2} = (\sqrt{32})^{2}\\ 4^{x} = 32\\ 2^{2}^{x} = 2^{5}\\ x=5/2$

$log125_{0,04} = \\ 0,04^{x} = 125 \\ \frac{4}{100} ^{x} = 125\\ \frac{2}{50} ^{x} = 125\\ \frac{1}{25} ^{x} = 125\\ 25 ^{-x} = 125\\ 5^{2} ^ ^{-x}} = 5^{3} \\ 5^{-2x} = 5^{3} \\ -2x=3 \\ x=-3/2$

4+5/2-3/2
4+2/2
4+1=5