Question

Log ( 3 ) (x ^ { 2 } -5x-3)=1​

Answer 1

Решил методом интегрирования правой части уравнениями

Answer 2

To solve the equation $\log_3(x^2 - 5x - 3) = 1$, you can use the properties of logarithms to isolate $x$.

First, rewrite the equation using the definition of a logarithm:

$\log_3(x^2 - 5x - 3) = 1$

This equation essentially says that $3^1$ is equal to $x^2 - 5x - 3$, because the logarithm with base 3 raised to the power of 1 gives you 3.

So, you have:

$3^1 = x^2 - 5x - 3$

Now, simplify the left side:

$3 = x^2 - 5x - 3$

Next, move all terms to one side of the equation to set it equal to zero:

$x^2 - 5x - 3 - 3 = 0$

Combine like terms:

$x^2 - 5x - 6 = 0$

Now, you have a quadratic equation. You can solve it by factoring, completing the square, or using the quadratic formula. In this case, factoring is straightforward:

$(x - 6)(x + 1) = 0$

Now, set each factor equal to zero and solve for $x$:

1. $x - 6 = 0$ => $x = 6$

2. $x + 1 = 0$ => $x = -1$

So, the solutions to the equation are $x = 6$ and $x = -1$.