Question

3ln(x)+5ln(3)=(3/x)
solve for x.

Answer 1

The solution to the equation
`\(3\ln(x) + 5\ln(3) = (3)/(x)\)` is
`\(x = 1\)`.

To solve the equation
`\(3\ln(x) + 5\ln(3) = (3)/(x)\)` for
`\(x\)`, we can follow these steps:

1. Combine logarithmic terms:

`\[ \ln(x^3) + \ln(3^5) = (3)/(x) \]`

2. Combine logarithmic terms further:

`\[ \ln\left(3^5 \cdot x^3\right) = (3)/(x) \]`

3. Set the expression equal to
`\((3)/(x)\)`:

`\[ 3x = (3)/(x) \]`

Now, solve for
`\(x\)`:

`\[ 3x^2 = 3 \]`

Divide both sides by 3:

`\[ x^2 = 1 \]`

Take the square root of both sides:

`\[ x = \pm 1 \]`

However, since the natural logarithm is only defined for positive values, we discard the negative solution.

Therefore, the solution to the equation
`\(3\ln(x) + 5\ln(3) = (3)/(x)\)` is
`\(x = 1\)`.