Question

(1/18)^x+1=18^x. Помогите, пожалуйста, как делать?

Answer 1

Х1= ㏒18((1+√5)/2)
х1= ㏒18((1-√5)/2)

Answer 2

Solving the Equation (1/18)^x + 1 = 18^x

To solve the equation (1/18)^x + 1 = 18^x, we can follow these steps:

1. Isolate the Exponential Terms: - Subtract 1 from both sides of the equation to isolate the exponential terms.

2. Take the Natural Logarithm: - Take the natural logarithm of both sides of the equation to solve for x.

3. Solve for x: - Use properties of logarithms to solve for x.

Let's solve the equation step by step.

Step 1: Isolate the Exponential Terms

Subtract 1 from both sides of the equation: ``` (1/18)^x = 18^x - 1 ```

Step 2: Take the Natural Logarithm

Take the natural logarithm of both sides of the equation: ``` ln((1/18)^x) = ln(18^x - 1) ```

Step 3: Solve for x

Use properties of logarithms to solve for x: ``` x * ln(1/18) = ln(18^x - 1) x = ln(18^x - 1) / ln(1/18) ```

This is the general approach to solving the given equation. If you have specific values for x or need further assistance with the calculation, feel free to provide additional details for a more tailored solution.