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If \(5^{x-2}=125\), what is the value of \(x\)?यदि \(5^{x-2}=125\) है, तो \(x\) का मान क्या होगा?
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Correct answer:सही उत्तर: 55
Since \(125=5^3\), the equation becomes \(5^{x-2}=5^3\). With equal bases, the exponents are equal, so \(x-2=3\), giving \(x=5\). Exam tip: rewrite the numerical side as a power of the same base before equating exponents.\(125=5^3\) लिख सकते हैं। इसलिए \(5^{x-2}=5^3\) होने पर समान आधारों की घातें बराबर होंगी: \(x-2=3\)। अतः \(x=5\)। परीक्षा में पहले दाएँ पक्ष की संख्या को उसी आधार की घात के रूप में लिखें।
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