If (25^{x}=5^6), then (x=)?
Answer and explanation
Correct answer: (3)
Since 25 can be written as a power of 5, \(25=5^2\). Therefore, \(25^x=(5^2)^x=5^{2x}\). In \(5^{2x}=5^6\), the bases are equal, so the exponents must be equal: \(2x=6\), giving \(x=3\). Hence, option B is correct. Exam tip: When exponential expressions have the same base, equate their exponents.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
Since 25 can be written as a power of 5, \(25=5^2\). Therefore, \(25^x=(5^2)^x=5^{2x}\). In \(5^{2x}=5^6\), the bases are equal, so the exponents must be equal: \(2x=6\), giving \(x=3\). Hence, option B is correct. Exam tip: When exponential expressions have the same base, equate their exponents.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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