Question

вычислить
㏒ₐ√ᵃᵇ, если ㏒ₐᵇ=8

Answer 1

$log_{a} \sqrt{ab} = log_{a}\sqrt{a} + log_{a} \sqrt{b} = \frac{1}{2} + \frac{1}{2} log_{a}b = \frac{1}{2} + \frac{1}{2} \times 8 = \frac{1}{2} + 4 = 4\frac{1}{2}$

Answer 2

$log_{a}( \sqrt{ab} ) = log_{ a}( {ab})^{ \frac{1}{2} } = \frac{1}{2} log_{a}(ab) = \\ \\ = \frac{1}{2} log_{a}(a) + \frac{1}{2 } log_{a}(b) = \frac{1}{2} + \frac{1}{2} \times 8 = \\ \\ = 0.5 + 4 = 4.5$



ОТВЕТ: 4,5