Question

Помогите решить: 1) 3^x - 3^(x-2) = 72 2) log3(x^2 -7x+15) = 2 3)3^(x^2-7x+10)>3^-2 4)3^(x-1) + 3^(x-2) + 3^(x-3) =3159

Answer 1

Решение смотри на фотографии

Answer 2

1. 3^x - 3^(x-2) = 72

First, we can simplify the equation by using the properties of exponents:

3^x - 3^(x-2) = 3^x - (1/9) * 3^x = (8/9) * 3^x

Now we can rewrite the equation as:

(8/9) * 3^x = 72

Multiplying both sides by (9/8), we get:

3^x = 81

Taking the logarithm base 3 of both sides, we obtain:

x = 4

Therefore, the solution to the equation is x = 4.

2. log3(x^2 - 7x + 15) = 2

We can rewrite the equation in exponential form:

3^2 = x^2 - 7x + 15

9 = x^2 - 7x + 15

Subtracting 9 from both sides, we get:

x^2 - 7x + 6 = 0

Factoring the left-hand side, we obtain:

(x - 6)(x - 1) = 0

Therefore, the solutions to the equation are x = 6 and x = 1.

3. 3^(x^2-7x+10) > 3^-2

We can simplify the right-hand side of the inequality as:

3^-2 = 1/9

Now we can rewrite the inequality as:

3^(x^2-7x+10) > 1/9

Taking the logarithm base 3 of both sides, we obtain:

x^2 - 7x + 10 < -2

Rearranging the terms, we get:

x^2 - 7x + 12 < 0

Factoring the left-hand side, we obtain:

(x - 3)(x - 4) < 0

Therefore, the solutions to the inequality are:

3 < x < 4

4. 3^(x-1) + 3^(x-2) + 3^(x-3) = 3159

We can simplify the left-hand side of the equation as:

3^(x-3) * (3^3 + 3^2 + 3^1) = 39 * 3^(x-3)

Now we can rewrite the equation as:

39 * 3^(x-3) = 3159

Dividing both sides by 39, we get:

3^(x-3) = 81

Taking the logarithm base 3 of both sides, we obtain:

x - 3 = 4

Therefore, the solution to the equation is x = 7.