Question

Log3(x+4)=log3(5x+2) Можно более подробное обьяснение

Answer 1

Основания одинаковые, поэтому можно приравнять и решить, как простое уравнение.

Answer 2

Уравнение log3(x+4) = log3(5x+2) может быть решено путем применения свойств логарифмов. Давайте разберемся подробнее.

Решение уравнения log3(x+4) = log3(5x+2):

1. Используем свойство лог#### Solving the Equation Log3(x+4) = log3(5x+2)

To solve the equation Log3(x+4) = log3(5x+2), we can use the properties of logarithms to simplify and solve for the value of x.

First, let's start by understanding the properties of logarithms. The equation Log3(x+4) = log3(5x+2) can be solved using the fact that if loga(b) = loga(c), then b = c.

Solution Steps:

1. Apply the Property of Logarithms: - Since both sides of the equation are logarithms with the same base, we can equate the arguments inside the logarithms. - This gives us the equation x + 4 = 5x + 2.

2. Solve for x: - Now, we can solve for x by rearranging the equation and isolating x on one side.

Let's proceed with solving the equation using the steps outlined above.

Solution:

1. Apply the Property of Logarithms: - Equating the arguments inside the logarithms gives us: - x + 4 = 5x + 2.

2. Solve for x: - Rearranging the equation: - 4 = 5x - x + 2 - 4 = 4x + 2 - 4 - 2 = 4x - 2 = 4x - x = 2

Conclusion:

The solution to the equation Log3(x+4) = log3(5x+2) is x = 2.