Question

9×16^x-7×12^x-16×9^x=0​

Answer 1

Решение:
9 * 16^x - 7 * 12^x - 16 * 9^x=0
разделим на 9^x
9*(4/3)^(2x)-7*(4/3)^x-16=0
пусть (4/3)^x=t; t> 0
9t²-7t-16=0
t1=16/9
t2=-1 - посторонний корень
(4/3)^x=16/9
(4/3)^x=(4/3)²
x=2

Answer 2

To solve the equation 9×16^x - 7×12^x - 16×9^x = 0, we can use a substitution method. Let's rewrite the equation using variables:

Let a = 16^x and b = 12^x. Then the equation becomes:

9a - 7b - 16(ab) = 0

Now we have a quadratic equation in terms of a and b. Let's solve it:

9a - 7b - 16(ab) = 0

Rearranging the terms:

16(ab) = 9a - 7b

Dividing both sides by ab:

16 = (9a - 7b)/(ab)

Now, let's substitute a = 16^x and b = 12^x back into the equation:

16 = (9(16^x) - 7(12^x))/(16^x)(12^x)

Now we have an equation in terms of x. Let's simplify it further:

16 = (9(2^4)^x - 7(2^2)^x)/((2^4)^x(2^2)^x)

16 = (9(2^(4x)) - 7(2^(2x)))/(2^(4x))(2^(2x))

16 = (9(2^(4x)) - 7(2^(2x)))/(2^(4x+2x))

16 = (9(2^(4x)) - 7(2^(2x)))/(2^(6x))

Now we can see that the equation is in terms of the exponential function with base 2. To simplify it further or find a numerical solution, we need to make additional assumptions or use numerical methods.