Question

Lg (9-x)+2 lg 1/x+3=0

Answer 1

Ответ:

Решение на фотографии

Answer 2

To solve the equation LG(9 - x) + 2LG(1/x + 3) = 0, we need to simplify it and find the value(s) of x that satisfy the equation.

First, let's apply the properties of logarithms to simplify the equation:

Using the property log(a) + log(b) = log(ab):

LG(9 - x) + LG((1/x + 3)^2) = 0

Applying the property log(a^b) = b * log(a):

LG((9 - x)(1/x + 3)^2) = 0

Now, let's remove the logarithm by converting it back to exponential form:

(9 - x)(1/x + 3)^2 = 10^0

Simplifying further:

(9 - x)(1/x + 3)^2 = 1

Expanding the square:

(9 - x)(1/x + 3)(1/x + 3) = 1

Now, we can solve for x by setting each factor to zero:

9 - x = 0 or 1/x + 3 = 0 or 1/x + 3 = -1

Solving the first equation:

9 - x = 0 x = 9

For the second equation:

1/x + 3 = 0 1/x = -3 x = -1/3

For the third equation:

1/x + 3 = -1 1/x = -4 x = -1/4

Therefore, the solutions to the equation are x = 9, x = -1/3, and x = -1/4.