Question

Log3(x) - log9(x) =2​

Answer 1

log3(x)-log3^2(x)=2

log3(x)-1/2log3(x)=2

1/2log3(x)=2

log3(x)=4

x=3^4

x=81

Answer 2

$log_{3}(x) - log_{9}(x) = 2$

1)Выражаем 9 как 3 в степени 2

$log_{3}(x) - log_{3 {}^{2} }(x) = 2$

2)Логарифм степени равен произведению показателя степени на логарифм её основания

$log_{3}(x) - \frac{1}{2} log_{3}(x) = 2$

3)Объединяем 1 и log(3,x)

$log_{3}(x) - \frac{1 \times log_{3}(x) }{2} = 2$

4)Избавляемся от дробей в log(3,x)-(1log(3,x)) /2=2 умножение обеих частей на НОЗ

$2 log_{3}(x) - 1 log_{3}(x) = 4$

5)Добавляем 2log(3,x) и - 1log(3,x)

$1 log_{3}(x) = 4$

6)Перемещаем множетели, не имеющие х их левой части уравнения

$log_{3}(x) = 4$

7)log(b,x)=a; x=b^a

$x = {3}^{4}$

8)

$x = 81$

Answer 3

To solve the equation log3(x) - log9(x) = 2, we can use the properties of logarithms.

First, let's simplify the equation using the property of logarithms that states log(a) - log(b) = log(a/b):

log3(x) - log9(x) = 2

log3(x/9) = 2

Next, we can rewrite the equation in exponential form using the definition of logarithms. If loga(b) = c, then a^c = b:

3^2 = x/9

9 = x/9

To solve for x, we can cross multiply:

9 * 9 = x

81 = x

Therefore, the solution to the equation log3(x) - log9(x) = 2 is x = 81.