Question

Log3(1+log1/3x)=1 помогите пж

Answer 1

Решение
Log3(1+log1/3x)=1 
x > 0
1 + log₁/₃ x = 3¹
 log₁/₃ x = 3 - 1
log₁/₃ x = 2
x = (1/3)²
x = 1/9

Answer 2

Solving the Equation Log3(1+log1/3x)=1

To solve the equation Log3(1+log1/3x)=1, we can follow these steps:

1. First, we can rewrite the equation using logarithmic properties. 2. Then, we can solve for the variable x.

Let's proceed with the solution.

Step 1: Rewrite the Equation

We can rewrite the given equation using logarithmic properties. The equation Log3(1+log1/3x)=1 can be rewritten as:

1 + log(1/3x) = 3

Step 2: Solve for x

Now, we can solve for the variable x by isolating it in the equation.

log(1/3x) = 3 - 1

log(1/3x) = 2

To solve for x, we need to exponentiate both sides of the equation. Since the base of the logarithm is 1/3, we will use 1/3 as the base for exponentiation.

1/3^(log(1/3x)) = 1/3^2

1/3^(log(1/3x)) = 1/9

This simplifies to:

1/3x = 1/9

Now, we can solve for x:

x = (1/9) / (1/3)

x = (1/9) * (3/1)

x = 1/3

So, the solution to the equation Log3(1+log1/3x)=1 is x = 1/3.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.