Question

log(x+3)-log(x-3)=1 ​

Answer 1

Answer:

$\dfrac{3\left(e+1\right)}{e-1}$

Step-by-step explanation:

Assuming $log$ is the natural logarithm with base $e$, the Euler's constant.

$\log{\left(x+3\right)} - \log{\left(x-3\right)} = 1$

$\Rightarrow \log{\dfrac{x+3}{x-3}} = 1$ [Using the logarithmic property: $\log{\alpha} - \log{\beta} = \log{\dfrac{\alpha}{\beta}}$ ]

$\Rightarrow \dfrac{x+3}{x-3} = e$

$\Rightarrow x+3 = e\left(x-3\right) = ex - 3e$

$\Rightarrow x - ex = -3e - 3$

$\Rightarrow \left(1-e\right)x = -3\left(e + 1\right)$

$\Rightarrow x = \dfrac{-3\left(e+1\right)}{-\left(e-1\right)} = \boxed{\dfrac{3\left(e+1\right)}{e-1}}$