3*7^x-3^y=12 7^x×3^y=15

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вопрос

To solve this system of equations, we can rewrite the second equation as:

7^x 3^y = 15
(3^y / 3^y) 7^x 3^y = 15
7^x 3^y / 3^y = 15
7^x = 15 * 3^y

Now substitute this into the first equation:

3 (15 3^y) - 3^y = 12
45 3^y - 3^y = 12
44 3^y = 12
3^y = 12 / 44
3^y = 3 / 11
y = log3(3/11)

Now substitute this value of y back into the equation 7^x = 15 * 3^y:

7^x = 15 * 3^(log3(3/11))

We can simplify the right side by using the properties of logarithms:

7^x = 15 3^(log3(3) - log3(11))
7^x = 15 3^1 / 3^log3(11)
7^x = 15 * 3 / 11
7^x = 45 / 11
x = log7 (45 / 11)

Therefore, the solution to the system of equations is x = log7 (45 / 11) and y = log3 (3 / 11).