Question 22

If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?

Solution

$$1 < \log_{3}5 < 2$$
=> $$ 1 < \log_{5}(2 + x) < 2 $$
=> $$ 5 < 2 + x < 25$$
=> $$ 3 < x < 23$$

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