Question

Qual é o log 1000
0,01

Answer 1

$log_{0.01}(1000) \\ \\ {0.01}^{x} = 1000 \\ \\ { (\frac{1}{100}) }^{x} = {10}^{3} \\ \\ {( \frac{1}{ {10}^{2} } )}^{x} = {10}^{3} \\ \\ { (\frac{1}{10}) }^{2x} = {10}^{3} \\ \\ {10}^{ - 2x} = {10}^{3} \\ \\ - 2x = 3 \\ \\ - x = \frac{3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \times ( - 1)\\ \\ x = - \frac{3}{2}$