Question

вычислить
㏒ₐ√ᵃᵇ, если ㏒ₐᵇ=8

Answer 1

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

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