Question

Допоможіть будь ласка! 100 балів (@manyny06)

Answer 1

$log_{0.3}(9) - 2 \times log_{0.3}(10) =log_{0.3}(9) + log_{0.3}(10 {}^{ - 2} ) = log_{0.3}(9 \times 0.01) = log_{0.3}(0.09) = log_{0.3}((0.3) {}^{2} ) = 2$

$\frac{ log_{10}(72) - log_{10}(9) }{log_{10}(28) - log_{10}(7)} = \frac{log_{10}(72 \div 9)}{log_{10}(28 \div 7)} = \frac{log_{10}(8)}{log_{10}(4)} = \frac{log_{10}(2 {}^{3} )}{log_{10}(2 {}^{2} )} = \frac{3log_{10}(2)}{2log_{10}(2)} = 1.5$

$\frac{ log_{3}(16) }{log_{3}(4)} = \frac{log_{3}( {4}^{2} )}{log_{3}(4)} = \frac{2log_{3}( {4})}{log_{3}(4)} = 2$

$log_{3}(125) \times log_{5}(9) = log_{3}(5 {}^{3} ) \times log_{5}(3 {}^{2} ) = 3 \times 2 \times log_{3}(5) \times log_{5}(3) = 6$