Question

Решить уравнение 1-log5(x+3)=log525- это основание

Answer 1

Log5(5/(x+3))=log(5)2
5/(x+3)=2
5=2x+6
2x=-4
x=-2

Answer 2

Solving the Equation 1-log5(x+3)=log525

To solve the equation 1-log5(x+3)=log525, we can follow these steps:

1. Isolate the Logarithmic Term: - Start by isolating the logarithmic term on one side of the equation.

2. Use Properties of Logarithms: - Apply the properties of logarithms to simplify the equation.

3. Solve for x: - Once the equation is simplified, solve for the variable x.

Let's proceed with solving the equation step by step.

Step 1: Isolate the Logarithmic Term

We start with the equation 1-log5(x+3)=log525. To isolate the logarithmic term, we can add log5(x+3) to both sides of the equation.

Step 2: Use Properties of Logarithms

After adding log5(x+3) to both sides, the equation becomes: 1 = log5(x+3) + log525

We can simplify the right-hand side of the equation using the properties of logarithms, specifically the product rule of logarithms.

Step 3: Solve for x

Once the equation is simplified, we can solve for the variable x.

Let's proceed with the calculations based on the given equation and the steps outlined above.

1 = log5(x+3) + log525 1 = log5(5(x+3))

Now, we can rewrite the equation in exponential form: 5^1 = 5(x+3)

Solving for x: 5 = 5(x+3) 1 = x+3 x = 1-3 x = -2

So, the solution to the equation 1-log5(x+3)=log525 is x = -2.

This solution is based on the given equation and the standard properties of logarithms.

[[SOURCE #1]]