# ( x2 + 6x-3) x2-4x = (5-x)x2-4x

32x+3- 6.3x+1- 9 = 0

6log5=a and 5log4=b

4log0,24=…..

Are these 4 separate questions?

Convert the second equation to

25.7 x = 5

then divide both sides by 25.7.

Show your work and we will be glad to critique it for you

## Yes, these are four separate questions. I will address each question individually.

Question 1: (x^2 + 6x - 3) * (x^2 - 4x) = (5 - x) * (x^2 - 4x)

To solve this equation, you can expand and combine like terms on both sides of the equation.

First, expand both sides:

x^4 - 4x^3 + 6x^3 - 24x^2 - 3x^2 + 12x = 5x^2 - 20x - x^3 + 4x^2

Next, combine like terms:

x^4 + 2x^3 - 27x^2 + 20x = 9x^2 - 20x

Now, move all terms to one side of the equation to get:

x^4 + 2x^3 - 36x^2 = 0

This is a fourth-degree polynomial equation. To solve it, you can try factoring, using the rational root theorem, or using numerical methods like graphing or a calculator.

Question 2: 32x + 3 - 6.3x + 1 - 9 = 0

To simplify and solve this equation, combine like terms:

32x - 6.3x + 3 + 1 - 9 = 0

25.7x - 5 = 0

To solve for x, move the constant term to the right side:

25.7x = 5

Finally, divide both sides of the equation by 25.7:

x = 5/25.7

Simplifying the right-hand side gives:

x ≈ 0.1945 (rounded to four decimal places)

Question 3: 6log5 = a and 5log4 = b

To solve for a and b:

For the first equation, divide both sides by 6:

log5 = a/6

For the second equation, divide both sides by 5:

log4 = b/5

These equations cannot be further simplified unless you know the value of log5 or log4. If you provide the values, I can compute the answers accordingly.

Question 4: 4log0.24 = ?

To evaluate this logarithmic expression, you can use the properties of logarithms. Specifically, you can rewrite log0.24 as the logarithm of the reciprocal of 0.24 (which is 1/0.24) and then apply the power rule of logarithms.

Start by rewriting the expression:

4log0.24 = 4log(1/0.24)

Next, using the power rule of logarithms, write the expression as:

4(-log0.24)

Finally, you can evaluate -log0.24 using a calculator or a logarithmic table to get the numerical value.