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1. If $5^{(x + 3)} = 2 5^{(3 x - 4)}$ then the value of x is = ?

A. $\frac{5}{11}$

B. $\frac{11}{5}$

C. $\frac{11}{3}$

D. $\frac{13}{5}$

Solution:

\begin{aligned} 5^{(x + 3)} = 2 5^{(3 x - 4)} \\ \Rightarrow 5^{(x + 3)} = {(5^{2})}^{(3 x - 4)} \\ \Rightarrow 5^{(x + 3)} = {5^{2}}^{(3 x - 4)} \\ \Rightarrow 5^{(x + 3)} = 5^{(6 x - 8)} \\ \Rightarrow x + 3 = 6 x - 8 \\ \Rightarrow 5 x = 11 \\ \Rightarrow x = \frac{11}{5} \end{aligned}

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