Find the value of x for which
Question:

Find the value of $x$ for which $\left(\frac{5}{3}\right)^{-4} \times\left(\frac{5}{3}\right)^{-5}=\left(\frac{5}{3}\right)^{3 x}$.

Solution:

Consider the left side:

$\left(\frac{5}{3}\right)^{-4} \times\left(\frac{5}{3}\right)^{-5}=\left(\frac{5}{3}\right)^{(-4+(-5))}=\left(\frac{5}{3}\right)^{-9}$

Given:

$\left(\frac{5}{3}\right)^{-9}=\left(\frac{5}{3}\right)^{3 x}$

Comparing the powers:

$-9=3 x \Rightarrow x=-3$

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