Question

\log_{3}x-\log_{3}(x+2)=3​

Answer 1

Answer:

The answer is given equation does not have any real solution

Step-by-step explanation:

Given equation is

            $\log_3x-\log_3(x+2)=3$

           $\Rightarrow \log_3\frac{x}{x+2}=3$, since $\log a-\log b=\log\frac{a}{b}$

          $\Rightarrow \frac{x}{x+2}=3^3=27$, since $\log_ax=y\Rightarrow x=a^y$

          $\Rightarrow x=27x+54\\\Rightarrow 27x-x=-54\\\Rightarrow 26x=-54\\\Rightarrow x=-\frac{27}{13}$

But $\log_3x$ to be defined x must be positive, hence above answer must be discarded.

Hence no solution.