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1. If $\log_{5} (x^{2} + x) -$ $\log_{5} (x + 1)$ = 2, then the value of x is -

A. 5

B. 10

C. 25

D. 32

Solution:

\begin{aligned} \log_{5} (x^{2} + x) - \log_{5} (x + 1) = 2 \\ \Rightarrow \log_{5} (\frac{x^{2} + x}{x + 1}) = 2 \\ \Rightarrow \log_{5} [\frac{x (x + 1)}{x + 1}] = 2 \\ \Rightarrow \log_{5} x = 2 \\ \Rightarrow x = 5^{2} \\ = 25 \end{aligned}

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