Question

log ³√25 na base 0,2

Answer 1

log(0,2) ³√25 = x
(0,2)^x = ³√25
(1/5)^x = 25^1/3
(5-¹)x = (5²)^1/3
5^(-x) = 5^(2/3)
-x = 2/3
x = -2/3 ✓

Answer 2

$log_{0.2}( \sqrt[3]{25} ) = log_{0.2}( \sqrt[3]{ {5}^{2} } ) = \\ = log_{0.2}( {5}^{ \frac{2}{3} } ) = \frac{2}{3} \times log_{0.2}(5) = \\ = \frac{2}{3} \times \frac{ log_{5}(5) }{ log_{5}(0.2) } = \frac{2}{3} \times \frac{1}{ log_{5}( \frac{1}{5} ) } = \\ = \frac{2}{3} \times \frac{1}{ log_{5}( {5}^{ - 1} ) } = \frac{2}{3} \times \frac{1}{ - 1 \times log_{5}(5) } \\ = \frac{2}{3} \times \frac{1}{ - 1 \times 1} = \frac{2}{3} \times \frac{1}{ - 1} = \frac{2}{3} \times ( - 1) \\ =\boxed{ - \frac{2}{3} }$