If 125^{x} = frac{25}{5^{x}}, then find the v | vedclass

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Question

(C) Given the equation: $125^{x} = \frac{25}{5^{x}}$Express all terms with base $5$:$(5^{3})^{x} = \frac{5^{2}}{5^{x}}$Using the power of a power rule

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) Given the equation: $125^{x} = \frac{25}{5^{x}}$Express all terms with base $5$:$(5^{3})^{x} = \frac{5^{2}}{5^{x}}$Using the power of a power rule $(a^{m})^{n} = a^{mn}$:$5^{3x} = 5^{2} \cdot 5^{-x}$Using the product rule $a^{m} \cdot a^{n} = a^{m+n}$:$5^{3x} = 5^{2-x}$Since the bases are equal,equate the exponents:$3x = 2 - x$$3x + x = 2$$4x = 2$$x = \frac{2}{4} = \frac{1}{2}$

If $125^{x} = \frac{25}{5^{x}},$ then find the value of $x$.

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