Question

0,3x - 4 - x < 7,2 - 8x; 4^x - 3^x+1 = 4^x-1 + 3; lg(x-4)+lg(x+3)=lg(5+4)

Answer 1

Ответ:

С третьим непонятно это натуральный логарифм?

Answer 2

Let's solve each equation step by step:

1. 0.3x - 4 - x < 7.2 - 8x

To simplify the equation, let's combine like terms:

-0.7x - 4 < 7.2 - 8x

Add 8x to both sides:

7.3x - 4 < 7.2

Add 4 to both sides:

7.3x < 11.2

Divide both sides by 7.3 to isolate x:

x < 11.2 / 7.3

x < 1.534

Therefore, the solution to the inequality is x < 1.534.

2. 4^x - 3^(x+1) = 4^(x-1) + 3

Let's simplify the equation by using some properties of exponents:

4^x - 3 * 3^x = 4^(x - 1) + 3

Now let's simplify further:

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

Multiply both sides by 4 to eliminate the fraction:

4^(x + 1) - 3 * 3^x = 4^x + 12

Let's rewrite 3 * 3^x as 3^(x + 1):

4^(x + 1) - 3^(x + 1) = 4^x + 12

Since we have the same base on both sides (4 and 3), we can equate the exponents:

x + 1 = x + 12

Subtract x from both sides:

1 = 12

This is not a true statement. Therefore, the equation has no solution.

3. lg(x - 4) + lg(x + 3) = lg(5 + 4)

Let's simplify the equation using the properties of logarithms:

lg((x - 4)(x + 3)) = lg(9)

Since the logarithm function is one-to-one, we can drop the logarithm on both sides:

(x - 4)(x + 3) = 9

Expanding the left side:

x^2 - x - 12 = 9

Rearranging the equation:

x^2 - x - 21 = 0

Now let's solve this quadratic equation by factoring or using the quadratic formula. Factoring gives:

(x - 4)(x + 3) = 0

Setting each factor equal to zero:

x - 4 = 0 or x + 3 = 0

x = 4 or x = -3

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

Please note that I have solved the equations to the best of my ability based on the information provided.