вычислить ㏒ₐ√ᵃᵇ, если ㏒ₐᵇ=8. Created by nikivladqwedc. algebra-ru

вычислить ㏒ₐ√ᵃᵇ, если ㏒ₐᵇ=8...

July 2022 2 13 Report

вычислить
㏒ₐ√ᵃᵇ, если ㏒ₐᵇ=8

snow99

Verified answer

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

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Mihail001192

Verified answer

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

ОТВЕТ: 4,5

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