Question

Решите систему!!! log5x+log2y=13 log5x"4+log 1/2y=2 очень подробно!!! пожалуйста!!!!!!!

Answer 1

Применена замена переменной, свойства логарифмов

Answer 2

Solving the System of Equations Involving Logarithms

To solve the system of equations log5x + log2y = 13 and log5x"4 + log(1/2)y = 2, we can use the properties of logarithms to simplify and solve for the variables x and y.

First, let's simplify the given equations using the properties of logarithms.

1. Simplify the First Equation: - The sum of logarithms is equal to the logarithm of the product, so we can rewrite the first equation as: - log5x + log2y = 13 becomes log(5x * 2y) = 13.

2. Simplify the Second Equation: - The sum of logarithms is equal to the logarithm of the product, so we can rewrite the second equation as: - log5x"4 + log(1/2)y = 2 becomes log(5x^4) + log(1/2)y = 2.

Now that we have simplified the given equations, we can proceed to solve for x and y.

3. Combine the Simplified Equations: - We can combine the simplified equations to form a single equation: - log(5x * 2y) = 13 and log(5x^4) + log(1/2)y = 2.

4. Use the Power Rule of Logarithms: - The power rule of logarithms states that log_b(x^n) = n * log_b(x). We can apply this rule to simplify the combined equation.

5. Solve for x and y: - After simplifying the combined equation, we can solve for the variables x and y.

Let's proceed with the calculations and simplifications based on the given equations and properties of logarithms.

I will now perform the calculations and simplifications based on the given equations and properties of logarithms to solve for the variables x and y.