Question

Log2 (4-x)=7 log5 (x+3)+ log5 4=log5 16 log4 (2-x) = log4 5 log2 (5x-7) - log2 5=log2 21

Answer 1

Ответ:

решение на фото......

Answer 2

To solve the given equations, we'll work on them one by one.

Equation 1: log2(4 - x) = 7 log5(x + 3) + log5(4)

We'll convert the logarithmic equation into exponential form to simplify it.

2^(log2(4 - x)) = 2^(7 log5(x + 3) + log5(4))

4 - x = (x + 3)^7 * 4

4 - x = 4 * (x + 3)^7

4 - x = 4 * (x + 3)^7

Expand the right side of the equation:

4 - x = 4 * (x^7 + 3^7 + 7 * 3^6 * x + 21 * 3^5 * x^2 + 35 * 3^4 * x^3 + 35 * 3^3 * x^4 + 21 * 3^2 * x^5 + 7 * 3 * x^6 + x^7)

Rearrange the equation and simplify:

4 - x = 4x^7 + 4 * 3^7 + 28 * 3^6 * x + 84 * 3^5 * x^2 + 140 * 3^4 * x^3 + 140 * 3^3 * x^4 + 84 * 3^2 * x^5 + 28 * 3 * x^6 + x^7

Combine like terms and bring everything to one side:

x^7 + 28x^6 + 84 * 3x^5 + 140 * 3^2 * x^4 + 140 * 3^3 * x^3 + 84 * 3^4 * x^2 + 28 * 3^5 * x + 4x - 4 + 4 * 3^7 = 0

Simplify further if needed, but this is the general form of the equation. Unfortunately, it does not have a simple algebraic solution.

Equation 2: log4(2 - x) = log4(5)

Since both sides have the same base (4), we can equate the arguments:

2 - x = 5

Solve for x:

-x = 5 - 2

x = -3

Equation 3: log2(5x - 7) - log2(5) = log2(21)

Combine the logarithms using the quotient rule:

log2((5x - 7)/5) = log2(21)

Since the bases are the same, we can equate the arguments:

(5x - 7)/5 = 21

Multiply both sides by 5:

5x - 7 = 21 * 5

5x - 7 = 105

Add 7 to both sides:

5x = 105 + 7

5x = 112

Divide both sides by 5:

x = 112/5

x = 22.4

Therefore, the solutions to the equations are:

• Equation 1 does not have a simple algebraic solution.
• Equation 2: x = -3
• Equation 3: x = 22.4