Question

4^x-9^y=7 3*2^x=4*3^y решить систему!

Answer 1

3×2^x=4×3^y
3x×2^x×2^2×3^y
3^y+1×x×2^x+2

Answer 2

To solve the system of equations:

1. 4^x - 9^y = 7
2. 3 * 2^x = 4 * 3^y

We can use the fact that 9 is equal to 3^2, and rewrite the equations accordingly:

1. 4^x - (3^2)^y = 7
2. 3 * 2^x = 4 * 3^y

Now, let's solve the system step by step:

Step 1: Simplify the equations

1. 4^x - 3^(2y) = 7
2. 3 * 2^x = 4 * 3^y

Step 2: Express 4 as 2^2 in the first equation

1. (2^2)^x - 3^(2y) = 7
2. 3 * 2^x = 4 * 3^y

Step 3: Apply the power rule (a^(m*n) = (a^m)^n)

1. 2^(2x) - 3^(2y) = 7
2. 3 * 2^x = 4 * 3^y

Step 4: Rewrite the second equation in terms of powers of 2

2^(x + 1) = 3^(y + 1)

Step 5: Since we have two equations and two variables, we can try to equate the exponents to solve for x and y:

From the second equation, we can see that the exponents on both sides are equal:

x + 1 = y + 1

Step 6: Solve for y in terms of x:

y = x

Step 7: Substitute y with x in the first equation:

2^(2x) - 3^(2x) = 7

Step 8: Now we have a single equation with one variable. We can solve for x.

Let's try to find an integer solution for x (and subsequently, y):

x = 1: 2^(21) - 3^(21) = 4 - 9 = -5 (Not a solution)

x = 2: 2^(22) - 3^(22) = 16 - 81 = -65 (Not a solution)

x = 3: 2^(23) - 3^(23) = 64 - 729 = -665 (Not a solution)

x = 4: 2^(24) - 3^(24) = 256 - 6561 = -6305 (Not a solution)

x = 5: 2^(25) - 3^(25) = 1024 - 59049 = -58025 (Not a solution)

As we can see, there are no integer solutions for x (and y) that satisfy the given system of equations. It is possible that there might be non-integer solutions, but without further information, this is as far as we can go with the current equations.