Question

Lx-13l×log2 (x-3)=3 (13-x)

Answer 1

|x-13|×log2 (x-3)=3 (13-x)

одз x>3

1. x>3 x<13

(13 - x)*log(2) (x - 3) = 3*(13 - x)

Сокращаем на 13 - х ≠ 0

log(2) (x - 3) = 3

x - 3 = 8

x = 11

3 < 11 < 13 корен

2. x >= 13

(13 - x)*log(2) (x - 3) = 3*(13 - x)

(13 - x)(log(2) (x - 3) - 3) = 0

x = 13 да корень >= 13

log(2)(x - 3) = 3   x = 11 не корень < 13

ответ 11 и 13

Answer 2

To solve the equation $Lx - 13\log_2(x - 3) = 3(13 - x)$, you can follow these steps:

1. Distribute on the right side:

   $Lx - 13\log_2(x - 3) = 39 - 3x$

2. Move all terms to one side of the equation to set it to zero:

   $Lx - 13\log_2(x - 3) + 3x - 39 = 0$

3. Combine like terms:

   $Lx + 3x - 13\log_2(x - 3) - 39 = 0$

4. Solve for $x$:

   $4x - 13\log_2(x - 3) - 39 = 0$

   This equation is transcendental, meaning it involves a logarithm. Transcendental equations don't usually have simple closed-form solutions. You may need to use numerical methods or graphical methods to find an approximate solution. Software like Python with libraries such as SymPy or numerical solvers can help with this.

If you have specific values for $L$, you can substitute those in and use a numerical method to find the value of $x$.