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If \(2^{x+1}=64\), what is the value of \(x\)?यदि \(2^{x+1}=64\) हो, तो \(x\) का मान क्या है?
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Correct answer:सही उत्तर: 55
Since \(64=2^6\), the equation becomes \(2^{x+1}=2^6\), so \(x+1=6\). Therefore, \(x=5\). Choosing 6 is a common mistake because it is the value of \(x+1\), not \(x\). In the exam, first express both sides with the same base and then equate the exponents.क्योंकि \(64=2^6\), इसलिए \(2^{x+1}=2^6\) से \(x+1=6\) प्राप्त होता है। अतः \(x=5\)। विकल्प C में 6 लेने की सामान्य गलती होती है, क्योंकि वह \(x+1\) का मान है, \(x\) का नहीं। परीक्षा में समान आधार वाली घातों को बराबर करते समय घातांक की तुलना करें।
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