Question

Log 3 (х^2-4)=log 3 (4x-7)

Answer 1

Объяснение:

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Answer 2

To solve the given equation, we have a logarithmic equation with the same base on both sides. This allows us to set the arguments of the logarithms equal to each other and solve for the variable x.

Given equation: log3(x^2 - 4) = log3(4x - 7)

Using the property of logarithms that states log_b(a) = log_b(c) if and only if a = c, we can set the arguments inside the logarithms equal to each other:

x^2 - 4 = 4x - 7

Now, let's solve for x:

x^2 - 4x + 3 = 0

This is a quadratic equation. We can factor it or use the quadratic formula to find the solutions:

(x - 3)(x - 1) = 0

This equation has two possible solutions:

1. x - 3 = 0 => x = 3
2. x - 1 = 0 => x = 1

So, the solutions to the given equation are x = 3 and x = 1.