Предмет: Математика, автор: anastasialebedeva10

Найдите значение выражения (log49x)2, если log7x3 = 2.

Ответы

Автор ответа: Minsk00

Найдите значение выражения (log₄₉x)², если log₇x³ = 2.

Решение
Найдем в начале чему равен log₇x
Используем правило logₐbⁿ = nlogₐb
log₇x³ = 3log₇x
Так как
log₇x³ = 2
то
3log₇x = 2
log₇x = 2/3
Находим
(log₄₉x)²
Используем правило
$log_{a^n}b= \frac{1}{n}log_ab$

$(log_{49}x)^2= (log_{7^2}x)^2 = (\frac{1}{2}log_7x)^2=(\frac{1}{2}* \frac{2}{3})^2=( \frac{1}{3} )^2= \frac{1}{9}$

Ответ: (log₄₉x)²=1/9

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