Question

Log3(x^2+6)=log3 (5x)

Answer 1

Ответ:

x=2 x=3

Объяснение:

Answer 2

$log_{3}( {x}^{2} + 6 ) = log_{3}(5x) \\ {x}^{2} + 6 > 0 \\ 5x > 0 \\ {x}^{2} + 6 = 5x \\ {x}^{2} - 5x + 6 = 0 \\ x = 2 \\ x = 3$

Ответ: 2, 3.

Answer 3

To solve the equation log3(x^2 + 6) = log3(5x), we can use the properties of logarithms. Since both sides of the equation have the same base (log3), we can set the arguments of the logarithms equal to each other:

x^2 + 6 = 5x

Now, we have a quadratic equation. To solve for x, we need to bring all terms to one side and then factor or use the quadratic formula. Let's rearrange the equation:

x^2 - 5x + 6 = 0

Now, we can factor the quadratic equation:

(x - 2)(x - 3) = 0

Setting each factor equal to zero gives us two possible solutions:

x - 2 = 0 => x = 2 x - 3 = 0 => x = 3

So, the solutions for the equation log3(x^2 + 6) = log3(5x) are x = 2 and x = 3.